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%I #9 Jan 18 2019 04:44:50
%S 41,73,193,521,761,2273,6073,8513,10169,22697,37889,73361,80153,
%T 221201,351913,1879601,2321881,4259641,6395201,8212553,9619081,
%U 11282657,36087833,59502977,72496049,236886401,556953841,809098513,830450161,888024649,2420631793,3845317297,13243533449,17279669993,29704278649,49624610521,59974491817,107046777121,158191301329
%N Primes 8k + 1 at the end of the maximal gaps in A269424.
%C Subsequence of A007519.
%C A269424 lists the corresponding record gap sizes. See more comments there.
%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 + 1 are 17 and 41, so a(1)=41. The next prime of this form is 73 and the gap 73-41=32 is a new record, so a(2)=73.
%o (PARI) re=0; s=17; forprime(p=41, 1e8, if(p%8!=1, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)
%Y Cf. A007519, A269424, A269425.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Feb 25 2016