|
| |
|
|
A073276
|
|
Irregular primes (A000928) with irregularity index one.
|
|
5
| |
|
|
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; 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.
|
|
|
REFERENCES
| 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.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000 (from Buhler et al.)
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 * A105460 A141851 A105461
Adjacent sequences: A073273 A073274 A073275 * A073277 A073278 A073279
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 22 2002
|
| |
|
|
