A073276 Irregular primes (A000928) with irregularity index one.

37, 59, 67, 101, 103, 131, 149, 233, 257, 263, 271, 283, 293, 307, 311, 347, 389, 401, 409, 421, 433, 461, 463, 523, 541, 557, 577, 593, 607, 613, 619, 653, 659, 677, 683, 727, 751, 757, 761, 773, 797, 811, 821, 827, 839, 877, 881, 887, 953, 971, 1061, 1091

Offset

1,1

Comments

A prime p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p.

In other words, irregular primes p dividing the numerator of B(2k) for a single k, 1<=k<(p-1)/2.

Links

T. D. Noe, Table of n, a(n) for n=1..10000 (from Buhler et al.)

J. Buhler, R. Crandall, R. Ernvall, T. Metsankyla and M. A. Shokrollahi, Irregular Primes and Cyclotomic Invariants to 12 Million, J. Symbolic Computation 31, 2001, 89-96.

Bernoulli numbers, irregularity index of primes

Mathematica

Do[p = Prime[n]; k = 1; c = 0; While[ 2*k < p - 3, If[ Mod[ Numerator[ BernoulliB[2*k]], p] == 0, c++ ]; k++ ]; If[ c == 1, Print[p]], {n, 3, 200} ]

Crossrefs

Cf. A000928, A000367, A060974, A060975 and A073277.

Sequence in context: A109166 A090798 A000928 * A281290 A105460 A141851

Adjacent sequences: A073273 A073274 A073275 * A073277 A073278 A073279

Keyword

nonn

Author

Robert G. Wilson v, Jul 22 2002

Status

approved