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A092224
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Numbers k such that the numerator of Bernoulli(2*k) 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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COMMENTS
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103 = A094095(1) is the first irregular prime in A094095. This sequence is the union of 2 arithmetic progressions: (24 + 102*n)/2 and 103*n. Note that the numerator of BernoulliB(2*114) is divisible by the first nontrivial irregular squared prime 103^2, when A090943(1)/2 = a(n) = 114 = (24 + 102*2)/2. Also, the numerator of BernoulliB(2*1236) is divisible by 103^2 because a(n) = 1236 = (24 + 102*24)/2 = 103*24/2. - Alexander Adamchuk, Jul 31 2006
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LINKS
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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, Jul 31 2006 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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