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 A268800 #19 Jan 17 2019 02:55:13 %S A268800 3,11,31,83,283,383,1327,2591,7351,7759,11171,11587,31391,46919, %T A268800 147919,288023,360611,425603,507163,666203,1414703,2198887,3358151, %U A268800 9287659,11512547,11648531,24315047,42453823,145554779,161720147,184007671,766668811 %N A268800 Primes 4k + 3 preceding the maximal gaps in A268799. %C A268800 Subsequence of A002145. %C A268800 A268799 lists the corresponding record gap sizes. See more comments there. %H A268800 Alexei Kourbatov, <a href="/A268800/b268800.txt">Table of n, a(n) for n = 1..41</a> %H A268800 Alexei Kourbatov and Marek Wolf, <a href="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019. %e A268800 The first two primes of the form 4k+3 are 3 and 7, so a(1)=3. 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)=11. %o A268800 (PARI) re=0; s=3; forprime(p=7, 1e8, if(p%4!=3, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p) %Y A268800 Cf. A002145, A084161, A268799, A268801. %K A268800 nonn %O A268800 1,1 %A A268800 _Alexei Kourbatov_, Feb 13 2016