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%I #22 Jun 15 2020 20:13:41
%S 11,41,131,227,557,1151,1787,6449,7433,35729,148667,180959,402761,
%T 407153,2339297,5522039,11158331,20831621,22441073,27681671,73452191,
%U 241563941,953758661,1444258271,1917281867,6822754391,15867287129,28265030429,40841580683,177858260357
%N Primes 6k - 1 at the end of the maximal gaps in A268928.
%C Subsequence of A007528 and A334545.
%C A268928 lists the corresponding record gap sizes. See more comments there.
%H Alexei Kourbatov, <a href="/A268930/b268930.txt">Table of n, a(n) for n = 1..37</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) = A268928(n) + A268929(n). - _Alexei Kourbatov_, Jun 15 2020.
%e The first two primes of the form 6k-1 are 5 and 11, so a(1)=11. The next primes of this form are 17, 23, 29; the gaps 17-11 = 23-17 = 29-23 are not records so nothing is added to the sequence. The next prime of this form is 41 and the gap 41-29=12 is a new record, so a(2)=41.
%o (PARI) re=0; s=5; forprime(p=11, 1e8, if(p%6!=5, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)
%Y Cf. A007528, A268928, A268929, A334543, A334545.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Feb 15 2016