%I #11 Jan 18 2019 04:45:07
%N Primes 8k + 7 at the end of the maximal gaps in A269519.
%C Subsequence of A007522.
%C A269519 lists the corresponding record gap sizes. See more comments there.
%H Alexei Kourbatov, <a href="/A269521/b269521.txt">Table of n, a(n) for n = 1..39</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 + 7 are 7 and 23, so a(1)=23. The next primes of this form are 31, 47; the gaps 31-23 and 47-31 are not records so nothing is added to the sequence. The next prime of this form is 71 and the gap 71-47=24 is a new record, so a(2)=71.
%o (PARI) re=0; s=7; forprime(p=23, 1e8, if(p%8!=7, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)
%Y Cf. A007522, A269519, A269520.
%A _Alexei Kourbatov_, Feb 28 2016