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%I #16 Jul 18 2020 16:03:48
%S 13,31,61,271,1381,4423,7867,22273,24337,38557,40351,69661,480343,
%T 1164799,1207903,1468189,1526929,3976003,11962963,14466967,19097593,
%U 30098239,39895771,198389797,303644749,393202651,485949787,680676709,1917215533,3868901233,4899890383,6957510319,7599383353
%N Primes 6k + 1 at the end of the maximal gaps in A268925.
%C Subsequence of A002476 and A330855.
%C A268925 lists the corresponding record gap sizes. See more comments there.
%H Alexei Kourbatov, <a href="/A268927/b268927.txt">Table of n, a(n) for n = 1..36</a>
%H Alexei Kourbatov and Marek Wolf, <a href="https://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
%F a(n) = A268925(n) + A268926(n). - _Alexei Kourbatov_, Jun 21 2020
%e 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.
%o (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)
%Y Cf. A002476, A268925, A268926, A330853, A330855.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Feb 15 2016