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A073276 Irregular primes (A000928) with irregularity index one. 12
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 (list; graph; refs; listen; history; text; internal format)
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.
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
Sequence in context: A109166 A090798 A000928 * A281290 A105460 A141851
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jul 22 2002
STATUS
approved

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Last modified February 26 13:41 EST 2024. Contains 370352 sequences. (Running on oeis4.)