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%I #16 Jan 18 2019 15:21:53
%S 7,19,43,103,307,419,1367,2647,7411,7823,11239,11699,31511,47051,
%T 148063,288179,360779,425779,507347,666403,1414943,2199143,3358423,
%U 9287939,11512843,11648887,24315443,42454267,145555231,161720627,184008203,766669427
%N Primes 4k + 3 at the end of the maximal gaps in A268799.
%C Subsequence of A002145.
%C A268799 lists the corresponding record gap sizes. See more comments there.
%H Alexei Kourbatov, <a href="/A268801/b268801.txt">Table of n, a(n) for n = 1..41</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 4k+3 are 3 and 7, so a(1)=7. The next prime of this form is 11; the gap 11-7 is not a record so no term is added to the sequence. The next prime of this form is 19; the gap 19-11=8 is a new record so a(2)=19.
%o (PARI) re=0; s=3; forprime(p=7, 1e8, if(p%4!=3, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)
%Y Cf. A002145, A084161, A268799, A268800.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Feb 13 2016
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