The Syracuse Conjecture

(the Syracuse sequence for the numbers 1 to 200)






Jean-François COLONNA

www.lactamme.polytechnique.fr

jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K bug [Le bug de l'an 2000]]
[Do you believe that Real Numbers exist for a computer and that floating point computations are safe?]
[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 09/15/2017 and last updated on 06/19/2020 16:29:04 -CEST-)







And here are the sequences {U(n)} (each in reverse order) for U(0)=1 to U(0)=200, U(0) being the last number on each line (each U(0) is followed with the percentage of even U(n)):


U(0)=0151 (75.00%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0512,1024,0341,0682,0227,0454,0151}
U(0)=0150 (75.00%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170,0340,0113,0226,0075,0150}
U(0)=0075 (73.33%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170,0340,0113,0226,0075}
U(0)=0113 (76.92%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170,0340,0113}
U(0)=0170 (81.82%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085,0170}
U(0)=0085 (80.00%): {0001,0002,0004,0008,0016,0032,0064,0128,0256,0085}
U(0)=0128 (87.50%): {0001,0002,0004,0008,0016,0032,0064,0128}
U(0)=0168 (81.82%): {0001,0002,0004,0008,0016,0032,0064,0021,0042,0084,0168}
U(0)=0084 (80.00%): {0001,0002,0004,0008,0016,0032,0064,0021,0042,0084}
U(0)=0042 (77.78%): {0001,0002,0004,0008,0016,0032,0064,0021,0042}
U(0)=0021 (75.00%): {0001,0002,0004,0008,0016,0032,0064,0021}
U(0)=0064 (85.71%): {0001,0002,0004,0008,0016,0032,0064}
U(0)=0032 (83.33%): {0001,0002,0004,0008,0016,0032}
U(0)=0141 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0212,0424,0141}
U(0)=0186 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0140,0280,0093,0186}
U(0)=0093 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0140,0280,0093}
U(0)=0140 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0140}
U(0)=0163 (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)=0183 (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)=0199 (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)=0126 (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)=0063 (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)=0190 (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)=0095 (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)=0143 (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)=0189 (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)=0147 (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)=0195 (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)=0129 (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)=0194 (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)=0097 (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)=0146 (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)=0073 (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)=0110 (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)=0055 (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)=0166 (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)=0083 (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)=0125 (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)=0188 (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)=0165 (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)=0171 (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)=0193 (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)=0145 (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)=0109 (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)=0164 (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)=0108 (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)=0054 (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)=0027 (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)=0082 (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)=0041 (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)=0124 (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)=0062 (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)=0031 (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)=0094 (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)=0047 (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)=0142 (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)=0071 (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)=0107 (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)=0161 (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)=0121 (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)=0182 (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)=0091 (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)=0137 (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)=0103 (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)=0155 (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)=0175 (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)=0111 (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)=0167 (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)=0159 (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)=0162 (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)=0081 (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)=0122 (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)=0061 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184,0061}
U(0)=0184 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092,0184}
U(0)=0092 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0092}
U(0)=0120 (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)=0060 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015,0030,0060}
U(0)=0030 (68.42%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015,0030}
U(0)=0015 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046,0015}
U(0)=0046 (70.59%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023,0046}
U(0)=0023 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070,0023}
U(0)=0070 (73.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035,0070}
U(0)=0035 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106,0035}
U(0)=0106 (76.92%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053,0106}
U(0)=0053 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160,0053}
U(0)=0160 (81.82%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080,0160}
U(0)=0080 (80.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0080}
U(0)=0138 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0104,0208,0069,0138}
U(0)=0069 (73.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0104,0208,0069}
U(0)=0104 (76.92%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0104}
U(0)=0181 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0272,0544,0181}
U(0)=0180 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0045,0090,0180}
U(0)=0090 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0045,0090}
U(0)=0045 (70.59%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136,0045}
U(0)=0136 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068,0136}
U(0)=0068 (73.33%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0068}
U(0)=0117 (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)=0176 (73.68%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0176}
U(0)=0169 (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)=0127 (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)=0191 (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)=0102 (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)=0051 (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)=0154 (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)=0077 (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)=0116 (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)=0187 (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)=0105 (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)=0158 (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)=0079 (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)=0119 (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)=0179 (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)=0123 (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)=0185 (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)=0139 (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)=0157 (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)=0156 (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)=0078 (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)=0039 (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)=0118 (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)=0059 (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)=0178 (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)=0089 (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)=0134 (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)=0067 (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)=0101 (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)=0152 (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)=0177 (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)=0133 (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)=0200 (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)=0132 (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)=0066 (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)=0033 (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)=0100 (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)=0050 (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)=0025 (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)=0076 (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)=0038 (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)=0019 (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)=0058 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029,0058}
U(0)=0029 (68.42%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088,0029}
U(0)=0088 (72.22%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044,0088}
U(0)=0044 (70.59%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0044}
U(0)=0198 (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)=0099 (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)=0149 (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)=0174 (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)=0087 (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)=0131 (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)=0197 (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)=0153 (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)=0115 (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)=0173 (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)=0135 (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)=0114 (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)=0057 (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)=0172 (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)=0086 (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)=0043 (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)=0130 (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)=0065 (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)=0196 (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)=0098 (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)=0049 (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)=0148 (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)=0074 (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)=0037 (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)=0112 (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)=0056 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0056}
U(0)=0144 (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)=0072 (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)=0036 (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)=0018 (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)=0009 (65.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028,0009}
U(0)=0028 (68.42%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014,0028}
U(0)=0014 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007,0014}
U(0)=0007 (64.71%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022,0007}
U(0)=0022 (68.75%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011,0022}
U(0)=0011 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034,0011}
U(0)=0034 (71.43%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017,0034}
U(0)=0017 (69.23%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052,0017}
U(0)=0052 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026,0052}
U(0)=0026 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013,0026}
U(0)=0013 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0020,0040,0013}
U(0)=0040 (77.78%): {0001,0002,0004,0008,0016,0005,0010,0020,0040}
U(0)=0020 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0020}
U(0)=0192 (78.57%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024,0048,0096,0192}
U(0)=0096 (76.92%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024,0048,0096}
U(0)=0048 (75.00%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024,0048}
U(0)=0024 (72.73%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012,0024}
U(0)=0012 (70.00%): {0001,0002,0004,0008,0016,0005,0010,0003,0006,0012}
U(0)=0006 (66.67%): {0001,0002,0004,0008,0016,0005,0010,0003,0006}
U(0)=0003 (62.50%): {0001,0002,0004,0008,0016,0005,0010,0003}
U(0)=0010 (71.43%): {0001,0002,0004,0008,0016,0005,0010}
U(0)=0005 (66.67%): {0001,0002,0004,0008,0016,0005}
U(0)=0016 (80.00%): {0001,0002,0004,0008,0016}
U(0)=0008 (75.00%): {0001,0002,0004,0008}
U(0)=0004 (66.67%): {0001,0002,0004}
U(0)=0002 (50.00%): {0001,0002}
U(0)=0001 (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 about 3 even numbers for each odd one...


Copyright (c) Jean-François Colonna, 2017-2020.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2017-2020.