A268927 Primes 6k + 1 at the end of the maximal gaps in A268925.

13, 31, 61, 271, 1381, 4423, 7867, 22273, 24337, 38557, 40351, 69661, 480343, 1164799, 1207903, 1468189, 1526929, 3976003, 11962963, 14466967, 19097593, 30098239, 39895771, 198389797, 303644749, 393202651, 485949787, 680676709, 1917215533, 3868901233, 4899890383, 6957510319, 7599383353

Offset: 1

Author

Alexei Kourbatov, Feb 15 2016

Keywords

• nonn

Comments

Subsequence of A002476 and A330855.

A268925 lists the corresponding record gap sizes. See more comments there.

Examples

			The first two primes of the form 6k+1 are 7 and 13, so a(1)=13. The next prime of this form is 19; the gap 19-13 is not a record so nothing is added to the sequence. The next prime of this form is 31 and the gap 31-19=12 is a new record, so a(2)=31.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..36
• Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Crossrefs

Cf. A002476, A268925, A268926, A330853, A330855.

Programs

PARI

re=0; s=7; forprime(p=13, 1e8, if(p%6!=1, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)

Formula

a(n) = A268925(n) + A268926(n). - Alexei Kourbatov, Jun 21 2020