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%I #11 Jan 17 2019 18:32:49
%S 5,13,61,461,557,877,1301,2957,4261,4637,5869,7349,20549,20789,31741,
%T 60917,62213,201101,239597,307733,1158821,1475261,3059597,5155309,
%U 5388101,5452093,19313549,69685061,85431373,91539277,291294901,381464669,512257453,609941069,1126255597
%N Primes 8k + 5 preceding the maximal gaps in A269513.
%C Subsequence of A007521.
%C A269513 lists the corresponding record gap sizes. See more comments there.
%H Alexei Kourbatov, <a href="/A269514/b269514.txt">Table of n, a(n) for n = 1..44</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.
%e The first two primes of the form 8k + 5 are 5 and 13, so a(1)=5. The next prime of this form is 29 and the gap 29-13=16 is a new record, so a(2)=13.
%o (PARI) re=0; s=5; forprime(p=13, 1e8, if(p%8!=5, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p)
%Y Cf. A007521, A269513, A269515.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Feb 28 2016