%I #17 Mar 29 2021 08:02:28

%S 12,63,103,114,165,206,216,267,309,318,369,412,420,471,515,522,573,

%T 618,624,675,721,726,777,824,828,879,927,930,981,1030,1032,1083,1133,

%U 1134,1185,1236,1287,1338,1339,1389,1440,1442,1491,1542,1545,1593,1644,1648

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

%C 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

%H Amiram Eldar, <a href="/A092224/b092224.txt">Table of n, a(n) for n = 1..3700</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BernoulliNumber.html">Bernoulli Number</a>.

%t Select[ Range[ 1694], Mod[ Numerator[ BernoulliB[2# ]], 103] == 0 &]

%t Select[Union[Table[2n*103,{n,1,100}],Table[24+102*n,{n,0,100}]], #<=10000&]/2 (* _Alexander Adamchuk_, Jul 31 2006 *)

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

%Y Cf. A094095, A090943, A027641.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Feb 25 2004