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 A334545 #13 Jun 02 2020 22:13:32 %S A334545 11,41,131,227,383,557,1151,1787,4337,6449,7433,8363,9137,12893,35729, %T A334545 37781,58889,59879,97787,105863,130769,148667,153887,180959,220151, %U A334545 328271,402761,407153,416849,542441,780587,1138367,1294571,1444463,1463837,1604951 %N A334545 Primes of the form 6k - 1 at the end of first-occurrence gaps in A334543. %C A334545 Subsequence of A007528. Contains A268930 as a subsequence. First differs from A268930 at a(5)=383. %C A334545 A334543 lists the corresponding gap sizes; see more comments there. %H A334545 Alexei Kourbatov, <a href="/A334545/b334545.txt">Table of n, a(n) for n = 1..160</a> %H A334545 Alexei Kourbatov and Marek Wolf, <a href="https://arxiv.org/abs/2002.02115">On the first occurrences of gaps between primes in a residue class</a>, arXiv preprint arXiv:2002.02115 [math.NT], 2020. %F A334545 a(n) = A334543(n) + A334544(n). %e A334545 The first two primes of the form 6k-1 are 5 and 11, so we have a(1)=11. The next primes of this form are 17, 23, 29; the gaps 17-11 = 23-17 = 29-23 have size 6 which already occurred before; so nothing is added to the sequence. The next prime of this form is 41 and the gap size 41-29=12 has not occurred before, so a(2)=41. %o A334545 (PARI) isFirstOcc=vector(9999,j,1); s=5; forprime(p=11,1e8,if(p%6!=5,next); g=p-s; if(isFirstOcc[g/6], print1(p", "); isFirstOcc[g/6]=0); s=p) %Y A334545 Cf. A007528, A014320, A058320, A268930, A330855, A334543, A334544. %K A334545 nonn %O A334545 1,1 %A A334545 _Alexei Kourbatov_, May 05 2020