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

Author

Jeff Burch, Apr 18 2000

Keywords

• nonn

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]

Crossrefs

Cf. A054678, A054680; A276414.

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

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