A060975 Irregular primes with irregularity index three.

491, 617, 647, 1151, 1217, 1811, 1847, 2939, 3833, 4003, 4657, 4951, 6763, 7687, 8831, 9011, 10463, 10589, 12073, 13217, 14533, 14737, 14957, 15287, 15787, 15823, 16007, 17681, 17863, 18713, 18869, 20533, 20939, 24019, 24659, 25153, 26561

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated by Hart et al., terms 1..9824 from T. D. Noe, calculated by 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

William Hart, David Harvey and Wilson Ong, Irregular primes to two billion, Mathematics of Computation, Vol. 86, No. 308 (2017), pp. 3031-3049; also available at arXiv:1605.02398 [math.NT], 2016.

David Harvey, Irregular primes to two billion (includes a list of all primes less than 2^31).

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 == 3, Print[p]], {n, 3, 1000} ]
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 == 3, Print@p], {n, 3, 13887} ]

Crossrefs

Cf. A000928, A000367, A060974, A060975, A073276 and A073277.

Sequence in context: A056052 A051115 A273809 * A180457 A271664 A082079

Adjacent sequences: A060972 A060973 A060974 * A060976 A060977 A060978

Keyword

nonn

Author

Robert G. Wilson v, Jul 22 2002

Extensions

Extended by Robert G. Wilson v, Sep 20 2006

Status

approved