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 A078953 #17 Feb 21 2025 06:19:42
%S A078953 67,2377,21487,31177,65167,67927,81547,139297,166597,178597,185527,
%T A078953 305017,305407,321817,341947,390487,427417,448867,547357,600877,
%U A078953 635347,668527,693727,697507,752287,764887,783787,812347,819487,877867,1196857,1229197,1262617,1279177
%N A078953 Primes p such that the differences between the 5 consecutive primes starting with p are (4,2,6,4).
%C A078953 Equivalently, primes p such that p, p+4, p+6, p+12 and p+16 are consecutive primes.
%H A078953 Amiram Eldar, <a href="/A078953/b078953.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from R. J. Mathar)
%F A078953 a(n) == 7 (mod 30). - _Amiram Eldar_, Feb 21 2025
%e A078953 67 is in the sequence since 67, 71 = 67 + 4, 73 = 67 + 6, 79 = 67 + 12 and 83 = 67 + 16 are consecutive primes.
%t A078953 Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {4,2,6,4} &][[;;, 1]] (* _Amiram Eldar_, Feb 21 2025 *)
%o A078953 (PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 2 && p4 - p3 == 6 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 21 2025
%Y A078953 Subsequence of A078850. - _R. J. Mathar_, Feb 11 2013
%Y A078953 Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.
%K A078953 nonn
%O A078953 1,1
%A A078953 _Labos Elemer_, Dec 19 2002
%E A078953 Edited by _Dean Hickerson_, Dec 20 2002