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 A356223 #6 Aug 08 2022 15:55:04
%S A356223 2,6,15,79,68,121,162,445,416,971,836,987,2888,1891,1650,5637,5518,
%T A356223 4834,9237,8152,10045,21550,20248,20179,29914,36070,24237,53355,52873,
%U A356223 34206,103134,90190,63755,147861,98103,117467,209102,206423,124954,237847,369223
%N A356223 Position of n-th appearance of 2n in the sequence of prime gaps (A001223). If 2n does not appear at least n times, set a(n) = -1.
%C A356223 Prime gaps (A001223) are the differences between consecutive prime numbers. They begin: 1, 2, 2, 4, 2, 4, 2, 4, 6, ...
%e A356223 We need the first 15 prime gaps (1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6) before we reach the 3rd appearance of 6, so a(6) = 15.
%t A356223 nn=1000;
%t A356223 gaps=Differences[Array[Prime,nn]];
%t A356223 Table[Position[gaps,2*n][[n,1]],{n,Select[Range[nn],Length[Position[gaps,2*#]]>=#&]}]
%Y A356223 The first appearances are at A038664, seconds A356221.
%Y A356223 Diagonal of A356222.
%Y A356223 A001223 lists the prime gaps.
%Y A356223 A073491 lists numbers with gapless prime indices.
%Y A356223 A356224 counts divisors with gapless prime indices, complement A356225.
%Y A356223 A356226 = gapless interval lengths of prime indices, run-lengths A287170.
%Y A356223 Cf. A000005, A028334, A029709, A060681, A119313, A137921, A193829, A274121.
%K A356223 nonn
%O A356223 1,1
%A A356223 _Gus Wiseman_, Aug 04 2022