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 A218249 #53 Dec 02 2018 03:07:52
%S A218249 21,3,15,1,18,29,5,3,8,11,31,4,20,3,7,5,19,53,1,19,48,19,29,32,7,38,1,
%T A218249 43,12,33,52,16,8,38,15,1,19,7,1,23,28,30,22,8,1,7,1,52,14,56,10,26,
%U A218249 32,65,5,71,12,83,37,6
%N A218249 Difference sequence of A219096.
%C A218249 Each appearance of 1 represents a prime p for which the next 3 larger primes are p+6, p+12, and p+18. More generally, the sequence gives gap sizes, measured as the number of primes minus 1, between consecutive triples (p, p+6, p+12) and (q, q+6, q+12) of consecutive primes. Conjecture: Every positive integer except 2 occurs infinitely many times.
%H A218249 Clark Kimberling, <a href="/A218249/b218249.txt">Table of n, a(n) for n = 1..10000</a>
%e A218249 A219096 = (15, 36, 39, 54, 55, 73, ...), so that
%e A218249 A218249 = (21, 3, 15, 1, 18, 29, 5, ...).
%e A218249 The first 1 in A218249 represents the primes p(54)=251, p(55)=257, P(56)=263, P(57)=269.
%t A218249 z = 10000; t = Differences[Prime[Range[z]]];
%t A218249 f[n_] := If[t[[n + 1]] - t[[n]] == 0, t[[n]], 0]
%t A218249 u = Table[f[n], {n, 1, 5000}];
%t A218249 p = Flatten[Position[u, 6]] (* A219096 *)
%t A218249 Flatten[Differences[p]] (* A218249 *)
%Y A218249 Cf. A219096.
%K A218249 nonn,easy
%O A218249 1,1
%A A218249 _Clark Kimberling_, Mar 26 2013