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 A330855 #24 May 04 2020 21:25:57 %S A330855 13,31,61,271,307,1381,1531,1987,2437,4423,7867,10243,16831,22273, %T A330855 24337,38557,40351,43543,69661,75511,100927,119047,171403,195691, %U A330855 204301,250423,480343,577807,590593,1164799,1207903,1278997,1382419,1468189,1526929,1890019,2314591 %N A330855 Primes 6k + 1 at the end of first-occurrence gaps in A330853. %C A330855 Subsequence of A002476. Contains A268927 as a subsequence. First differs from A268927 at a(5)=307. %C A330855 A330853 lists the corresponding gap sizes; see more comments there. %H A330855 Alexei Kourbatov, <a href="/A330855/b330855.txt">Table of n, a(n) for n = 1..135</a> %H A330855 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 A330855 a(n) = A330853(n) + A330854(n). %e A330855 The first two primes of the form 6k+1 are 7 and 13, so a(1)=13. 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)=31. %o A330855 (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(p", "); isFirstOcc[g/6]=0); s=p) %Y A330855 Cf. A002476, A014320, A058320, A268927, A330853 (first-occurrence gap sizes), A330854 (primes beginning the first-occurrence gaps). %K A330855 nonn %O A330855 1,1 %A A330855 _Alexei Kourbatov_, Apr 27 2020