%I #19 Jul 18 2020 16:04:08

%S 7,19,43,241,1327,4363,7789,22189,24247,38461,40237,69499,480169,

%T 1164607,1207699,1467937,1526659,3975721,11962651,14466637,19097257,

%U 30097861,39895309,198389311,303644227,393202123,485949253,680676109,1917214927,3868900621,4899889741,6957509653,7599382573

%N Primes 6k + 1 preceding the maximal gaps in A268925.

%C Subsequence of A002476 and A330854.

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

%H Alexei Kourbatov, <a href="/A268926/b268926.txt">Table of n, a(n) for n = 1..36</a>

%H Alexei Kourbatov and Marek Wolf, <a href="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

%F a(n) = A268927(n) - A268925(n). - _Alexei Kourbatov_, Jun 21 2020

%e The first two primes of the form 6k+1 are 7 and 13, so a(1)=7. 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)=19.

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

%Y Cf. A002476, A268925, A268927, A330853, A330854.

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Feb 15 2016