%I #15 Mar 28 2015 14:52:34

%S 32,44,58,68,24,22,130,62,84,164,100,84,20,156,88,292,280,186,100,200,

%T 382,126,240,366,196,130,94,292,400,86,270,222,52,90,22,592,522,20,

%U 428,80,236,48,224,408,628,32,12,378,290,514,260,732,220,330,544,744,102

%N Smallest even index 2a such that n-th irregular prime p (A000928(n)) divides Bernoulli_{2a} with 0<=2a<=p-3.

%C 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 L. C. Washington, Introduction to Cyclotomic Fields, Springer, p. 350.

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

%e The first irregular prime (37) divides the numerator (-7709321041217) of the 32nd Bernoulli number.

%t 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 Cf. A000928, A000367, A035112, A046753, A189683, A189684, A189685.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Robert G. Wilson v_, May 12 2001