A092224 - OEIS

A092224

Numbers k such that the numerator of Bernoulli(2*k) is divisible by 103, the fifth irregular prime.

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

1,1

COMMENTS

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..3700

Eric Weisstein's World of Mathematics, Bernoulli Number.

MATHEMATICA

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 *)

CROSSREFS

Cf. A000928, A091216, A092221, A092222, A092223, A092225, A092226, A092227, A092228, A092229.

Cf. A094095, A090943, A027641.

Sequence in context: A196285 A196335 A349159 * A335252 A212509 A212249

Adjacent sequences: A092221 A092222 A092223 * A092225 A092226 A092227

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Feb 25 2004

STATUS

approved