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 A334543 #14 Jun 02 2020 22:11:55 %S A334543 6,12,18,30,24,36,42,54,48,60,84,66,78,72,126,90,102,108,114,96,120, %T A334543 150,138,162,132,144,168,246,156,180,186,240,204,192,216,198,210,174, %U A334543 258,252,222,234,228,318,282,264,276,342,306,294,312,270,354,372 %N A334543 First occurrences of gaps between primes 6k - 1: gap sizes. %C A334543 Contains A268928 as a subsequence. First differs from A268928 at a(5)=24. %C A334543 Conjecture: the sequence is a permutation of all positive multiples of 6, i.e., all positive terms of A008588. %C A334543 Conjecture: a(n) = O(n). See arXiv:2002.02115 (sect.7) for discussion. %H A334543 Alexei Kourbatov, <a href="/A334543/b334543.txt">Table of n, a(n) for n = 1..160</a> %H A334543 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 A334543 a(n) = A334545(n) - A334544(n). %e A334543 The first two primes of the form 6k-1 are 5 and 11, so a(1)=11-5=6. 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 41-29=12 has not occurred before, so a(2)=12. %o A334543 (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(g", "); isFirstOcc[g/6]=0); s=p) %Y A334543 Cf. A007528, A014320, A058320, A268928, A330853, A334544, A334545. %K A334543 nonn %O A334543 1,1 %A A334543 _Alexei Kourbatov_, May 05 2020