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 A330853 #24 May 04 2020 21:24:50 %S A330853 6,12,18,30,24,54,42,36,48,60,78,66,72,84,90,96,114,102,162,108,126, %T A330853 120,132,150,138,144,174,168,156,192,204,180,198,252,270,216,222,186, %U A330853 228,210,240,282,246,234,276,264,258,312,330,318,288,306,294,336,300,378 %N A330853 First occurrences of gaps between primes 6k+1: gap sizes. %C A330853 Contains A268925 as a subsequence. %C A330853 Conjecture: the sequence is a permutation of all positive multiples of 6, i.e., all positive terms of A008588. %C A330853 Conjecture: a(n) = O(n). See arXiv:2002.02115 (sect.7) for discussion. %H A330853 Alexei Kourbatov, <a href="/A330853/b330853.txt">Table of n, a(n) for n = 1..135</a> %H A330853 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 A330853 a(n) = A330855(n) - A330854(n). %e A330853 The first primes of the form 6k+1 are 7 and 13, so a(1)=13-7=6. The next prime 6k+1 is 19, and the gap 19-13=6 already occurred, so a new term is not added to the sequence. The next prime 6k+1 is 31, and the gap 31-19=12 is occurring for the first time; therefore a(2)=12. %o A330853 (PARI) isFirstOcc=vector(9999,j,1); s=7; forprime(p=13,1e8, if(p%6!=1,next); g=p-s; if(isFirstOcc[g/6], print1(g", "); isFirstOcc[g/6]=0); s=p) %Y A330853 Cf. A002476, A014320, A058320, A330854 (primes 6k+1 preceding the first-occurrence gaps), A330855 (primes 6k+1 at the end of the first-occurrence gaps). %K A330853 nonn %O A330853 1,1 %A A330853 _Alexei Kourbatov_, Apr 27 2020