A268930 Primes 6k - 1 at the end of the maximal gaps in A268928.

11, 41, 131, 227, 557, 1151, 1787, 6449, 7433, 35729, 148667, 180959, 402761, 407153, 2339297, 5522039, 11158331, 20831621, 22441073, 27681671, 73452191, 241563941, 953758661, 1444258271, 1917281867, 6822754391, 15867287129, 28265030429, 40841580683, 177858260357

Offset: 1

Author

Alexei Kourbatov, Feb 15 2016

Keywords

• nonn

Comments

Subsequence of A007528 and A334545.

A268928 lists the corresponding record gap sizes. See more comments there.

Examples

			The first two primes of the form 6k-1 are 5 and 11, so a(1)=11. The next primes of this form are 17, 23, 29; the gaps 17-11 = 23-17 = 29-23 are not records so nothing is added to the sequence. The next prime of this form is 41 and the gap 41-29=12 is a new record, so a(2)=41.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..37
• Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Crossrefs

Cf. A007528, A268928, A268929, A334543, A334545.

Programs

PARI

re=0; s=5; forprime(p=11, 1e8, if(p%6!=5, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)

Formula

a(n) = A268928(n) + A268929(n). - Alexei Kourbatov, Jun 15 2020.