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

1,1

Comments

Subsequence of A002476 and A330855.

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

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.

Formula

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

Example

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.

Prog

(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)

Crossrefs

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

Sequence in context: A155820 A242231 A330855 * A061239 A072023 A217614

Adjacent sequences: A268924 A268925 A268926 * A268928 A268929 A268930

Keyword

nonn

Author

Alexei Kourbatov, Feb 15 2016

Status

approved