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 A335367 #31 Jun 23 2025 21:59:15 %S A335367 3,5,11,29,97,127,149,211,541,907,1151,1361,1693,1847,2503,2999,4327, %T A335367 5623,9587,15727,16183,19373,19661,28277,30631,31469,31957,34123, %U A335367 35671,43391,44351,81509,82129,89753,134581,156007,162209,173429,188107,212777,265703 %N A335367 Primes at the end of the first-occurrence gaps in A014320. %C A335367 Contains A000101 as a subsequence. First differs from A000101 at a(7)=149. See A000101, A002386 and A005250 for more references and links. %H A335367 Brian Kehrig, <a href="/A335367/b335367.txt">Table of n, a(n) for n = 1..777</a> (Terms 1..745 from Alexei Kourbatov). %H A335367 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. %H A335367 The Prime Gap List, <a href="https://primegap-list-project.github.io/lists/prime-gaps-first-occurrences/">First Occurrence Prime Gaps</a> %F A335367 a(n) = A335366(n) + A014320(n). %e A335367 The first two primes are 2 and 3, and the first prime gap is 3 - 2 = 1; so a(1)=3. The next prime is 5, and the next gap is 5 - 3 = 2; this gap size has not occurred before, so a(2)=5. The next prime is 7, and the next gap is 7 - 5 = 2; the gap size 2 has already occurred before, so nothing is added to the sequence. %o A335367 (PARI) my(isFirstOcc=vector(9999, j, 1), s=2); forprime(p=3, 1e8, my(g=p-s); if(isFirstOcc[g], print1(p, ", "); isFirstOcc[g]=0); s=p) %Y A335367 Cf. A000101, A002386, A005250, A014320, A330853, A330854, A334543, A334544, A335366. %K A335367 nonn %O A335367 1,1 %A A335367 _Alexei Kourbatov_, Jun 03 2020