cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A180315 AbsoluteValue(Numerator(Bernoulli(2n))) mod denominator(Bernoulli(2n)).

Original entry on oeis.org

0, 1, 1, 1, 1, 5, 691, 1, 47, 775, 41, 17, 691, 1, 59, 12899, 47, 1, 638653, 1, 2011, 1, 53, 41, 14477, 5, 83, 775, 59, 53, 22298681, 1, 47, 62483, 1, 289, 48540859, 1, 1, 37, 47717, 77, 1058237, 1, 5407, 230759, 77, 1, 1450679, 1, 4471, 61, 83, 101, 71532367
Offset: 0

Views

Author

Robert G. Wilson v, Aug 27 2010

Keywords

Comments

From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.
Values sorted: 1, 5, 17, 37, 41, 47, 49, 53, 59, 61, 65, 77, 83, 89, 101, 113, 137, 161, 167, 169, 173, ..., .
a(n).==1 for n's: 1, 2, 3, 4, 7, 13, 17, 19, 21, 31, 34, 37, 38, 43, 47, 49, 57, 59, 61, 62, 67, 71, 73, ..., .
a(n).==5 for n's: 5, 25, 85, 185, 235, 295, 305, 335, 355, 365, 395, 425, 505, 535, 635, 685, 695, ..., .A051229
a(n)==17 for n's: 11, 77, 87, 121, 143, 187, 407, 517, 539, 649, 671, 737, 781, 847, 869, 1067, 1111, ..., .
a(n)==37 for n's: 39, 507, 1209, 1677, 3783, 4251, 5421, 5811, 6123, 6357, 6513, 7527, 7683, 7761, 8229, ..., .
a(n)==41 for n's: 10, 23, 123, 161, 170, 391, 437, 529, 610, 710, 851, 1010, 1081, 1127, 1357, 1403, ..., .
a(n)==47 for n's: 8, 16, 32, 64, 152, 248, 304, 376, 472, 496, 752, 824, 872, 992, 1256, 1336, 1504, ..., .
a(n)==49 for n's: 55, 275, 605, 2035, 3025, 3355, 3685, 3905, 4345, 5555, 5885, 6985, 7535, 7645, 8195, ..., .
a(n)==53 for n's: 22, 29, 203, 242, 374, 377, 493, 841, 899, 1073, 1247, 1298, 1342, 1363, 1562, 1711, ..., .
a(n)==59 for n's: 14, 28, 266, 434, 532, 868, 994, 1414, 1442, 1526, 1918, 2534, 2758, 2884, 2954, 3052, ..., .
a(n)==61 for n's: 51, 867, 2193, 3009, 3417, 6477, 7089, 8007, 8313, 8517, 10047, 10149, 11577, 11679, ..., .
a(n)==65 for n's: 159, 6837, 8427, 9381, 11289, 12561, 15423, 17331, 23691, 25917, 26553, 30687, 31323, ..., .
a(n)==77 for n's: 41, 46, 92, 287, 533, 697, 782, 874, 1058, 1517, 1681, 1748, 1927, 2116, 2162, 2419, ..., .
a(n)==83 for n's: 26, 52, 494, 988, 1534, 1586, 2626, 2678, 2782, 3068, 3172, 3562, 3874, 4082, 4342, ..., .
a(n)==89 for n's: 58, 1682, 1798, 2726, 3422, 5974, 7946, 8642, 8758, 9106, 12934, 13166, 13282, 13978, ..., .

Links

Crossrefs

Cf. A000367, A002445, A169980.

Programs

  • Mathematica
    f[n_] := Block[{b = BernoulliB[2 n]}, Mod[Abs@ Numerator@ b, Denominator@ b]]; Array[f, 53, 0]

Formula

|A000367(n)| mod A002445(n).

A180320 AbsoluteValue(Numerator(Bernoulli(4n))) - Numerator(Bernoulli(4n)) mod denominator(Bernoulli(4n)) divided by two.

Original entry on oeis.org

0, 1, 1, 691, 47, 41, 691, 59, 47, 638653, 2011, 53, 14477, 83, 59, 22298681, 47, 1, 48540859, 1, 47717, 1058237, 5407, 77, 1450679, 4471, 83, 71532367, 226439, 89, 971032651, 1, 47, 1310531, 167, 117419, 965295473, 179, 1, 522242099, 47717, 113
Offset: 0

Views

Author

Robert G. Wilson v, Aug 27 2010

Keywords

Comments

Sorted Values: 0, 1, 41, 47, 53, 59, 77, 83, 89, 113, 137, 167, 179, 197, 203, 209, 257, 293, 299, 323, 347, 377, 389, 413, 419, 497, 509, 533, 539, 587, 593, 599, ..., .

Crossrefs

Cf. A169980, A180315, A180321.

Programs

  • Mathematica
    f[n_] := Block[{b = BernoulliB[4 n]}, Mod[Abs@ Numerator@ b - Numerator@ b, Denominator@ b]/2]; Array[f, 60, 0]

A180321 (Numerator(Bernoulli(4n)) mod denominator(Bernoulli(4n)) - AbsoluteValue(Numerator(Bernoulli(4n))) mod denominator(Bernoulli(4n)))/4.

Original entry on oeis.org

0, 7, 7, 337, 104, 62, 337, 188, 104, 160471, 2377, 146, 4364, 356, 188, 3047342, 104, 7, 10754788, 7, 33644, 321959, 12649, 314, 400103, 6097, 356, 16531744, 304598, 398, 96547657, 7, 104, 396467, 944, 111158, 112780961, 1028, 7, 187526468, 33644
Offset: 0

Views

Author

Robert G. Wilson v, Aug 27 2010

Keywords

Comments

Sorted Values: 0, 7, 62, 104, 146, 188, 314, 337, 356, 398, 566, 734, 944, 1028, 1154, 1196, 1238, 1261, 1574, 1826, 1868, 2036, 2204, 2377, 2414, ..., .

Crossrefs

Cf. A169980, A180315, A180320.

Programs

  • Mathematica
    f[n_] := Block[{b = BernoulliB[4 n]}, (Mod[Numerator@b, Denominator@b] - Mod[Abs@Numerator@b, Denominator@b])/4]; Array[f, 60, 0]
Showing 1-3 of 3 results.

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