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.
%I A299467 #17 Oct 09 2019 20:57:03
%S A299467 58,3292,153640,12597148,846312184,52715297638,320040068824,
%T A299467 370475739904372,23170872799129498,532379740455157312,
%U A299467 111861518490094080436,1314934469494256636776,291496130251698265225984,7852328398132458266800348,1925603427201316655808983674
%N A299467 Least even integer k such that numerator(B_k) == 0 (mod 67^n).
%C A299467 67 is the third irregular prime. The corresponding entry for the first irregular prime 37 is A251782, and for the second irregular prime 59 is A299466.
%C A299467 The p-adic digits of the unique simple zero of the p-adic zeta function zeta_{(p,l)} with (p,l)=(67,58) were used to compute the sequence (see the Mathematica program below). This corresponds with Table A.2 in Kellner (2007). The sequence is increasing, but some consecutive entries are identical, e.g., entries 22 / 23 and 84 / 85. This is caused only by those p-adic digits that are zero.
%H A299467 Bernd C. Kellner, <a href="/A299467/b299467.txt">Table of n, a(n) for n = 1..100</a>
%H A299467 Bernd C. Kellner, <a href="http://www.bernoulli.org/">The Bernoulli Number Page</a>
%H A299467 Bernd C. Kellner, <a href="http://dx.doi.org/10.1090/S0025-5718-06-01887-4">On irregular prime power divisors of the Bernoulli numbers</a>, Math. Comp., 76 (2007), 405-441.
%H A299467 Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_prime#Irregular_pairs"> Irregular pairs</a>
%F A299467 Numerator(B_{a(n)}) == 0 (mod 67^n).
%e A299467 a(3) = 153640 because the numerator of B_153640 is divisible by 67^3 and there is no even integer less than 153640 for which this is the case.
%t A299467 p = 67; l = 58; LD = {49, 34, 42, 42, 39, 3, 62, 57, 19, 62, 10, 36, 14, 53, 57, 16, 60, 22, 41, 21, 25, 0, 56, 21, 24, 52, 33, 28, 51, 34, 60, 8, 47, 39, 42, 33, 14, 66, 50, 48, 45, 28, 61, 50, 27, 8, 30, 59, 32, 15, 3, 1, 54, 12, 30, 20, 14, 12, 10, 49, 33, 49, 54, 13, 26, 42, 8, 58, 12, 63, 19, 16, 48, 15, 2, 13, 1, 23, 2, 44, 64, 25, 40, 0, 16, 58, 44, 31, 62, 47, 61, 46, 9, 2, 50, 1, 62, 34, 31}; CalcIndex[L_, p_, l_, n_] := l + (p - 1) Sum[L[[i + 1]] p^i , {i, 0, n - 2}]; Table[CalcIndex[LD, p, l, n], {n, 1, Length[LD] + 1}] // TableForm
%Y A299467 Cf. 2*A091216, 2*A092230, A189683, A251782, A299466.
%K A299467 nonn
%O A299467 1,1
%A A299467 _Bernd C. Kellner_ and _Jonathan Sondow_, Feb 15 2018