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Search: id:A092224
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| A092224 |
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Numbers n such that numerator of Bernoulli(2n) is divisible by 103, the fifth irregular prime. |
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10
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| 12, 63, 103, 114, 165, 206, 216, 267, 309, 318, 369, 412, 420, 471, 515, 522, 573, 618, 624, 675, 721, 726, 777, 824, 828, 879, 927, 930, 981, 1030, 1032, 1083, 1133, 1134, 1185, 1236, 1287, 1338, 1339, 1389, 1440, 1442, 1491, 1542, 1545, 1593, 1644, 1648
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OFFSET
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1,1
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COMMENT
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103 = A094095[1] is the first irregular prime in A094095[n]. a(n) is a union of 2 arithmetic progressions: (24 + 102*n)/2 = {12,63,114,165,216,267,318,369,420,471,522,573,624,675,726,777,828,879,930,981,1032,1083,1134,1185,1236,...}, 103*n = {103,206,309,412,515,618,721,824,927,1030,1133,1236,...}. Note that Numerator[BernoulliB[2*114]] is divisible by the first nontrivial irregular prime square 103^2, when A090943[1]/2 = a(n) = 114 = (24 + 102*2)/2. Also the Numerator[BernoulliB[2*1236]] is divisible by 103^2 because a(n) = 1236 = (24 + 102*24)/2 = 103*24/2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 31 2006
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics..
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MATHEMATICA
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Select[ Range[ 1694], Mod[ Numerator[ BernoulliB[2# ]], 103] == 0 &]
Select[Union[Table[2n*103, {n, 1, 100}], Table[24+102*n, {n, 0, 100}]], #<=10000&]/2 - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 31 2006
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CROSSREFS
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Cf. A000928, A091216, A092221, A092222, A092223, A092225, A092226, A092227, A092228, A092229.
Cf. A094095, A090943, A027641.
Sequence in context: A005173 A045822 A065595 this_sequence A085463 A051922 A027810
Adjacent sequences: A092221 A092222 A092223 this_sequence A092225 A092226 A092227
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 25 2004
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