This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268927 #16 Jul 18 2020 16:03:48 %S A268927 13,31,61,271,1381,4423,7867,22273,24337,38557,40351,69661,480343, %T A268927 1164799,1207903,1468189,1526929,3976003,11962963,14466967,19097593, %U A268927 30098239,39895771,198389797,303644749,393202651,485949787,680676709,1917215533,3868901233,4899890383,6957510319,7599383353 %N A268927 Primes 6k + 1 at the end of the maximal gaps in A268925. %C A268927 Subsequence of A002476 and A330855. %C A268927 A268925 lists the corresponding record gap sizes. See more comments there. %H A268927 Alexei Kourbatov, <a href="/A268927/b268927.txt">Table of n, a(n) for n = 1..36</a> %H A268927 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 A268927 a(n) = A268925(n) + A268926(n). - _Alexei Kourbatov_, Jun 21 2020 %e A268927 The first two primes of the form 6k+1 are 7 and 13, so a(1)=13. The next prime of this form is 19; the gap 19-13 is not a record so nothing is added to the sequence. The next prime of this form is 31 and the gap 31-19=12 is a new record, so a(2)=31. %o A268927 (PARI) re=0; s=7; forprime(p=13, 1e8, if(p%6!=1, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p) %Y A268927 Cf. A002476, A268925, A268926, A330853, A330855. %K A268927 nonn %O A268927 1,1 %A A268927 _Alexei Kourbatov_, Feb 15 2016