A035112 - OEIS

A035112

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

32, 44, 58, 68, 24, 22, 130, 62, 84, 164, 100, 84, 20, 156, 88, 292, 280, 186, 100, 200, 382, 126, 240, 366, 196, 130, 94, 292, 400, 86, 270, 222, 52, 90, 22, 592, 522, 20, 428, 80, 236, 48, 224, 408, 628, 32, 12, 378, 290, 514, 260, 732, 220, 330, 544, 744, 102

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OFFSET

1,1

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..57.

Eric Weisstein's World of Mathematics, Irregular Pair

EXAMPLE

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

MATHEMATICA

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} ]

CROSSREFS

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

Sequence in context: A167528 A269230 A229115 * A308765 A236324 A211813

Adjacent sequences: A035109 A035110 A035111 * A035113 A035114 A035115

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Robert G. Wilson v, May 12 2001

STATUS

approved