The Syracuse Conjecture
(the Syracuse sequence for the numbers 1 to 256)
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
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- The Syracuse sequence is defined as follows:
U = N (an integer number [un nombre entier]) > 0
0
if U is even [si U est pair] :
n n
U
n
U = ----
n+1 2
else [sinon] :
U = 3*U + 1
n+1 n
- The Syracuse conjecture states that sooner or later the {[[4,] 2,] 1} sequence will appear
whatever the starting number N (and then repeats itself obviously ad vitam aeternam).
For example with U(0)=7:
U(0) = 7
U(1) = 22
U(2) = 11
U(3) = 34
U(4) = 17
U(5) = 52
U(6) = 26
U(7) = 13
U(8) = 40
U(9) = 20
U(10) = 10
U(11) = 5
U(12) = 16
U(13) = 8
U(14) = 4
U(15) = 2
U(16) = 1
Here are the sequences {U(n)} (each in reverse order) for U(0)=1 to U(0)=256, U(0) being the last number on each line (each U(0) is followed with the percentage of even U(n)):
U(0) = 201 (73.68%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0512,1024,0341,0682,0227,0454,0151,0302,0604,0201}
U(0) = 151 (75.00%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0512,1024,0341,0682,0227,0454,0151}
U(0) = 227 (78.57%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0512,1024,0341,0682,0227}
U(0) = 150 (75.00%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170,0340,0113,0226,0075,0150}
U(0) = 75 (73.33%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170,0340,0113,0226,0075}
U(0) = 226 (78.57%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170,0340,0113,0226}
U(0) = 113 (76.92%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170,0340,0113}
U(0) = 170 (81.82%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170}
U(0) = 85 (80.00%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085}
U(0) = 256 (88.89%): {0001,0002,0004,0008,0016,0032,0064,0128,0256}
U(0) = 128 (87.50%): {0001,0002,0004,0008,0016,0032,0064,0128}
U(0) = 168 (81.82%): {0001,0002,0004,0008,0016,0032,0064,0021,0042,0084,0168}
U(0) = 84 (80.00%): {0001,0002,0004,0008,0016,0032,0064,0021,0042,0084}
U(0) = 42 (77.78%): {0001,0002,0004,0008,0016,0032,0064,0021,0042}
U(0) = 21 (75.00%): {0001,0002,0004,0008,0016,0032,0064,0021}
U(0) = 64 (85.71%): {0001,0002,0004,0008,0016,0032,0064}
U(0) = 32 (83.33%): {0001,0002,0004,0008,0016,0032}
U(0) = 213 (78.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0320,0640,0213}
U(0) = 141 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0212,0424,0141}
U(0) = 212 (78.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0212}
U(0) = 186 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0140,0280,0093,0186}
U(0) = 93 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0140,0280,0093}
U(0) = 140 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0140}
U(0) = 217 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0368,0736,0245,0490,0163,0326,0652,0217}
U(0) = 163 (70.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0368,0736,0245,0490,0163}
U(0) = 245 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0368,0736,0245}
U(0) = 223 (64.79%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,1700,3400,1133,2266,0755,1510,0503,1006,0335,0670,0223}
U(0) = 207 (64.04%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,1052,2104,0701,1402,0467,0934,0311,0622,0207}
U(0) = 183 (63.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0620,1240,0413,0826,0275,0550,0183}
U(0) = 243 (63.92%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0548,1096,0365,0730,0243}
U(0) = 235 (63.28%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095,0190,0380,0760,0253,0506,1012,0337,0674,1348,0449,0898,0299,0598,0199,0398,0796,0265,0530,1060,0353,0706,0235}
U(0) = 199 (63.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095,0190,0380,0760,0253,0506,1012,0337,0674,1348,0449,0898,0299,0598,0199}
U(0) = 253 (63.64%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095,0190,0380,0760,0253}
U(0) = 252 (63.64%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095,0190,0063,0126,0252}
U(0) = 126 (63.30%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095,0190,0063,0126}
U(0) = 63 (62.96%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095,0190,0063}
U(0) = 190 (63.55%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095,0190}
U(0) = 95 (63.21%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143,0286,0095}
U(0) = 143 (63.46%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215,0430,0143}
U(0) = 215 (63.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0728,1456,0485,0970,0323,0646,0215}
U(0) = 189 (63.55%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0284,0568,0189}
U(0) = 147 (63.25%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0332,0664,0221,0442,0147}
U(0) = 221 (63.48%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0332,0664,0221}
U(0) = 195 (63.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110,0220,0440,0880,0293,0586,0195}
U(0) = 129 (63.11%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110,0220,0073,0146,0292,0097,0194,0388,0129}
U(0) = 194 (63.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110,0220,0073,0146,0292,0097,0194}
U(0) = 97 (63.03%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110,0220,0073,0146,0292,0097}
U(0) = 146 (63.25%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110,0220,0073,0146}
U(0) = 73 (62.93%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110,0220,0073}
U(0) = 220 (63.48%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110,0220}
U(0) = 110 (63.16%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055,0110}
U(0) = 55 (62.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166,0055}
U(0) = 166 (63.39%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083,0166}
U(0) = 83 (63.06%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250,0083}
U(0) = 250 (63.64%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125,0250}
U(0) = 125 (63.30%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188,0376,0125}
U(0) = 188 (63.55%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0188}
U(0) = 231 (63.28%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0248,0496,0992,1984,0661,1322,2644,0881,1762,0587,1174,0391,0782,1564,0521,1042,0347,0694,0231}
U(0) = 165 (63.39%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0248,0496,0165}
U(0) = 248 (63.64%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0248}
U(0) = 171 (63.20%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0164,0328,0109,0218,0436,0145,0290,0580,0193,0386,0772,0257,0514,0171}
U(0) = 193 (63.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0164,0328,0109,0218,0436,0145,0290,0580,0193}
U(0) = 145 (63.25%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0164,0328,0109,0218,0436,0145}
U(0) = 218 (63.48%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0164,0328,0109,0218}
U(0) = 109 (63.16%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0164,0328,0109}
U(0) = 164 (63.39%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0164}
U(0) = 216 (63.48%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0027,0054,0108,0216}
U(0) = 108 (63.16%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0027,0054,0108}
U(0) = 54 (62.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0027,0054}
U(0) = 27 (62.50%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082,0027}
U(0) = 82 (63.06%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041,0082}
U(0) = 41 (62.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124,0041}
U(0) = 124 (63.30%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062,0124}
U(0) = 62 (62.96%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031,0062}
U(0) = 31 (62.62%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094,0031}
U(0) = 94 (63.21%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047,0094}
U(0) = 47 (62.86%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142,0047}
U(0) = 142 (63.46%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071,0142}
U(0) = 71 (63.11%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214,0071}
U(0) = 214 (63.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107,0214}
U(0) = 107 (63.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161,0322,0107}
U(0) = 161 (63.64%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242,0484,0161}
U(0) = 242 (63.92%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121,0242}
U(0) = 121 (63.54%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182,0364,0121}
U(0) = 182 (63.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091,0182}
U(0) = 91 (63.44%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137,0274,0091}
U(0) = 137 (63.74%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206,0412,0137}
U(0) = 206 (64.04%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103,0206}
U(0) = 103 (63.64%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155,0310,0103}
U(0) = 155 (63.95%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233,0466,0155}
U(0) = 233 (64.29%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175,0350,0700,0233}
U(0) = 175 (64.20%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0668,1336,0445,0890,1780,0593,1186,0395,0790,0263,0526,0175}
U(0) = 222 (64.79%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0111,0222}
U(0) = 111 (64.29%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167,0334,0111}
U(0) = 167 (64.71%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251,0502,0167}
U(0) = 251 (65.15%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,3644,7288,2429,4858,1619,3238,1079,2158,0719,1438,0479,0958,0319,0638,1276,0425,0850,0283,0566,1132,0377,0754,0251}
U(0) = 159 (65.45%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,0607,1214,2428,0809,1618,0539,1078,0359,0718,0239,0478,0159}
U(0) = 239 (66.04%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0488,0976,0325,0650,1300,0433,0866,1732,0577,1154,2308,4616,9232,3077,6154,2051,4102,1367,2734,0911,1822,0607,1214,2428,0809,1618,0539,1078,0359,0718,0239}
U(0) = 162 (70.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0081,0162}
U(0) = 81 (69.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244,0081}
U(0) = 244 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122,0244}
U(0) = 122 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061,0122}
U(0) = 61 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061}
U(0) = 184 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184}
U(0) = 92 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092}
U(0) = 240 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015,0030,0060,0120,0240}
U(0) = 120 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015,0030,0060,0120}
U(0) = 60 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015,0030,0060}
U(0) = 30 (68.42%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015,0030}
U(0) = 15 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015}
U(0) = 46 (70.59%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046}
U(0) = 23 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023}
U(0) = 70 (73.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070}
U(0) = 35 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035}
U(0) = 106 (76.92%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106}
U(0) = 53 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053}
U(0) = 160 (81.82%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160}
U(0) = 80 (80.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080}
U(0) = 138 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0104,0208,0069,0138}
U(0) = 69 (73.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0104,0208,0069}
U(0) = 208 (78.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0104,0208}
U(0) = 104 (76.92%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0104}
U(0) = 241 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0272,0544,0181,0362,0724,0241}
U(0) = 181 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0272,0544,0181}
U(0) = 180 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0045,0090,0180}
U(0) = 90 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0045,0090}
U(0) = 45 (70.59%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0045}
U(0) = 136 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136}
U(0) = 68 (73.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068}
U(0) = 234 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0176,0352,0117,0234}
U(0) = 117 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0176,0352,0117}
U(0) = 176 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0176}
U(0) = 255 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0308,0616,0205,0410,0820,1640,3280,6560,13120,4373,8746,2915,5830,1943,3886,1295,2590,0863,1726,0575,1150,0383,0766,0255}
U(0) = 225 (66.04%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0308,0616,0205,0410,0820,1640,3280,1093,2186,4372,1457,2914,0971,1942,0647,1294,0431,0862,0287,0574,0191,0382,0127,0254,0508,0169,0338,0676,0225}
U(0) = 169 (66.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0308,0616,0205,0410,0820,1640,3280,1093,2186,4372,1457,2914,0971,1942,0647,1294,0431,0862,0287,0574,0191,0382,0127,0254,0508,0169}
U(0) = 254 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0308,0616,0205,0410,0820,1640,3280,1093,2186,4372,1457,2914,0971,1942,0647,1294,0431,0862,0287,0574,0191,0382,0127,0254}
U(0) = 127 (65.96%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0308,0616,0205,0410,0820,1640,3280,1093,2186,4372,1457,2914,0971,1942,0647,1294,0431,0862,0287,0574,0191,0382,0127}
U(0) = 191 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0308,0616,0205,0410,0820,1640,3280,1093,2186,4372,1457,2914,0971,1942,0647,1294,0431,0862,0287,0574,0191}
U(0) = 205 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0308,0616,0205}
U(0) = 204 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0051,0102,0204}
U(0) = 102 (69.23%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0051,0102}
U(0) = 51 (68.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154,0051}
U(0) = 154 (70.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077,0154}
U(0) = 77 (69.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232,0077}
U(0) = 232 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116,0232}
U(0) = 116 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0116}
U(0) = 249 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238,0476,0952,0317,0634,0211,0422,0844,0281,0562,0187,0374,0748,0249}
U(0) = 187 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238,0476,0952,0317,0634,0211,0422,0844,0281,0562,0187}
U(0) = 211 (67.50%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238,0476,0952,0317,0634,0211}
U(0) = 210 (67.50%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238,0079,0158,0316,0105,0210}
U(0) = 105 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238,0079,0158,0316,0105}
U(0) = 158 (67.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238,0079,0158}
U(0) = 79 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238,0079}
U(0) = 238 (68.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119,0238}
U(0) = 119 (67.65%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179,0358,0119}
U(0) = 179 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0404,0808,0269,0538,0179}
U(0) = 237 (68.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0356,0712,0237}
U(0) = 219 (66.04%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157,0314,0628,0209,0418,0836,1672,0557,1114,0371,0742,0247,0494,0988,0329,0658,0219}
U(0) = 247 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157,0314,0628,0209,0418,0836,1672,0557,1114,0371,0742,0247}
U(0) = 246 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157,0314,0628,0209,0418,0139,0278,0556,0185,0370,0123,0246}
U(0) = 123 (65.96%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157,0314,0628,0209,0418,0139,0278,0556,0185,0370,0123}
U(0) = 185 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157,0314,0628,0209,0418,0139,0278,0556,0185}
U(0) = 139 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157,0314,0628,0209,0418,0139}
U(0) = 209 (67.50%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157,0314,0628,0209}
U(0) = 157 (67.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236,0472,0157}
U(0) = 236 (68.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0236}
U(0) = 156 (67.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0039,0078,0156}
U(0) = 78 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0039,0078}
U(0) = 39 (65.71%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118,0039}
U(0) = 118 (67.65%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059,0118}
U(0) = 59 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178,0059}
U(0) = 178 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089,0178}
U(0) = 89 (67.74%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134,0268,0089}
U(0) = 134 (68.97%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067,0134}
U(0) = 67 (67.86%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202,0067}
U(0) = 202 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101,0202}
U(0) = 101 (69.23%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152,0304,0101}
U(0) = 152 (70.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0152}
U(0) = 177 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050,0100,0200,0400,0133,0266,0532,0177}
U(0) = 133 (68.97%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050,0100,0200,0400,0133}
U(0) = 200 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050,0100,0200}
U(0) = 132 (68.97%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050,0100,0033,0066,0132}
U(0) = 66 (67.86%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050,0100,0033,0066}
U(0) = 33 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050,0100,0033}
U(0) = 100 (69.23%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050,0100}
U(0) = 50 (68.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025,0050}
U(0) = 25 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076,0025}
U(0) = 76 (69.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038,0076}
U(0) = 38 (68.18%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019,0038}
U(0) = 19 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058,0019}
U(0) = 58 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058}
U(0) = 29 (68.42%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029}
U(0) = 88 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088}
U(0) = 44 (70.59%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044}
U(0) = 198 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0224,0448,0149,0298,0099,0198}
U(0) = 99 (69.23%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0224,0448,0149,0298,0099}
U(0) = 149 (70.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0224,0448,0149}
U(0) = 224 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0224}
U(0) = 174 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0296,0592,0197,0394,0131,0262,0087,0174}
U(0) = 87 (67.74%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0296,0592,0197,0394,0131,0262,0087}
U(0) = 131 (68.97%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0296,0592,0197,0394,0131}
U(0) = 197 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0296,0592,0197}
U(0) = 153 (67.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0260,0520,0173,0346,0115,0230,0460,0153}
U(0) = 230 (68.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0260,0520,0173,0346,0115,0230}
U(0) = 115 (67.65%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0260,0520,0173,0346,0115}
U(0) = 173 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0260,0520,0173}
U(0) = 135 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086,0172,0344,0688,0229,0458,0916,0305,0610,0203,0406,0135}
U(0) = 203 (67.50%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086,0172,0344,0688,0229,0458,0916,0305,0610,0203}
U(0) = 229 (68.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086,0172,0344,0688,0229}
U(0) = 228 (68.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086,0172,0057,0114,0228}
U(0) = 114 (67.65%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086,0172,0057,0114}
U(0) = 57 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086,0172,0057}
U(0) = 172 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086,0172}
U(0) = 86 (67.74%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043,0086}
U(0) = 43 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130,0043}
U(0) = 130 (68.97%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065,0130}
U(0) = 65 (67.86%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196,0065}
U(0) = 196 (70.37%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098,0196}
U(0) = 98 (69.23%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049,0098}
U(0) = 49 (68.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148,0049}
U(0) = 148 (70.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074,0148}
U(0) = 74 (69.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037,0074}
U(0) = 37 (68.18%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112,0037}
U(0) = 112 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056,0112}
U(0) = 56 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056}
U(0) = 144 (70.83%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0009,0018,0036,0072,0144}
U(0) = 72 (69.57%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0009,0018,0036,0072}
U(0) = 36 (68.18%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0009,0018,0036}
U(0) = 18 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0009,0018}
U(0) = 9 (65.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0009}
U(0) = 28 (68.42%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028}
U(0) = 14 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014}
U(0) = 7 (64.71%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007}
U(0) = 22 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022}
U(0) = 11 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011}
U(0) = 34 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034}
U(0) = 17 (69.23%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017}
U(0) = 52 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052}
U(0) = 26 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026}
U(0) = 13 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013}
U(0) = 40 (77.78%): {0001,0002,0004,0008,0016,0005,0010,0020,0040}
U(0) = 20 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020}
U(0) = 192 (78.57%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024,0048,0096,0192}
U(0) = 96 (76.92%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024,0048,0096}
U(0) = 48 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024,0048}
U(0) = 24 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024}
U(0) = 12 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012}
U(0) = 6 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0003,0006}
U(0) = 3 (62.50%): {0001,0002,0004,0008,0016,0005,0010,0003}
U(0) = 10 (71.43%): {0001,0002,0004,0008,0016,0005,0010}
U(0) = 5 (66.67%): {0001,0002,0004,0008,0016,0005}
U(0) = 16 (80.00%): {0001,0002,0004,0008,0016}
U(0) = 8 (75.00%): {0001,0002,0004,0008}
U(0) = 4 (66.67%): {0001,0002,0004}
U(0) = 2 (50.00%): {0001,0002}
U(0) = 1 (0.00%): {0001}
One can notice the high percentage of even U(n). It is obvious for on the one hand 3*U(n)+1 is even when U(n) is odd.
On the other hand, if U(n) is even then U(n)/2 is even with a 0.5 probability.
Then there should be more even numbers that odd ones...
See a related picture displaying the preceding values:
Copyright © Jean-François COLONNA, 2017-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2017-2024.