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 A035112 #16 Feb 16 2025 08:32:37
%S A035112 32,44,58,68,24,22,130,62,84,164,100,84,20,156,88,292,280,186,100,200,
%T A035112 382,126,240,366,196,130,94,292,400,86,270,222,52,90,22,592,522,20,
%U A035112 428,80,236,48,224,408,628,32,12,378,290,514,260,732,220,330,544,744,102
%N A035112 Smallest even index 2a such that n-th irregular prime p (A000928(n)) divides Bernoulli_{2a} with 0<=2a<=p-3.
%C A035112 The ordered pair (p(n),a(n)) where p(n) is the n-th irregular prime is called an irregular pair. Some irregular primes, such as 157, are in more than one pair. See A091887 for the number of pairs for each irregular prime. See A092681 and A092682 for higher-order irregular pairs. - _T. D. Noe_, Mar 03 2004
%D A035112 L. C. Washington, Introduction to Cyclotomic Fields, Springer, p. 350.
%H A035112 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrregularPair.html">Irregular Pair</a>
%e A035112 The first irregular prime (37) divides the numerator (-7709321041217) of the 32nd Bernoulli number.
%t A035112 Do[ p = Prime[ n ]; k = 1; While[ 2*k < p - 3 && Mod[ Numerator[ BernoulliB[ 2*k ] ], p ] != 0, k++ ]; If[ 2*k != p - 3, Print[ 2*k ] ], { n, 3, 200} ]
%Y A035112 Cf. A000928, A000367, A035112, A046753, A189683, A189684, A189685.
%K A035112 nonn
%O A035112 1,1
%A A035112 _N. J. A. Sloane_
%E A035112 More terms from _Robert G. Wilson v_, May 12 2001