A054679 First of n consecutive primes which differ by a multiple of 6.

2, 23, 47, 251, 1741, 1741, 19471, 118801, 148531, 148531, 406951, 1820111, 2339041, 19725473, 19725473, 73451737, 232301497, 400414121, 489144599, 489144599, 766319189, 766319189, 21549657539, 21549657539, 21549657539, 140432294381, 140432294381, 437339303279, 1552841185921, 1552841185921, 1552841185921

Offset

1,1

Comments

See A276414 for the indices of these primes. - M. F. Hasler, Sep 02 2016

The sequence is infinite, by Shiu's theorem. - Jonathan Sondow, Jun 22 2017

Links

Giovanni Resta, Table of n, a(n) for n = 1..35 (terms < 4*10^14) (corrected by Ray Chandler, Jan 19 2019)

J. K. Andersen, Consecutive Congruent Primes.

D. K. L. Shiu, Strings of Congruent Primes, J. Lond. Math. Soc. 61 (2) (2000) 359-373 [MR1760689]

Formula

a(n) = A000040(A276414(n)). - M. F. Hasler, Sep 02 2016

a(n) = min(A057620(n), A057621(n)) for all n >= 1. - M. F. Hasler, Sep 03 2016

Crossrefs

Cf. A054678, A054680; A276414.

Sequence in context: A105440 A139831 A049592 * A057621 A074809 A084237

Adjacent sequences: A054676 A054677 A054678 * A054680 A054681 A054682

Keyword

nonn

Author

Jeff Burch, Apr 18 2000

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Nov 09 2000

More terms from Jens Kruse Andersen, May 30 2006

Initial term and a(27)-a(31) added and name edited by M. F. Hasler, Sep 02 2016

Status

approved