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 A290488 #29 Aug 08 2017 16:48:10
%S A290488 2,7,47,181,467,526,1069,1262,1327,2477,3274,5119,12854,20809,28229,
%T A290488 31397,338038,520462,546391,1050631,1761206,1964987,3466943,6084986,
%U A290488 27348829,27915754,111108769,113652443,230126378,231902267,327764081,438981007,581755318,1837981547,2489382697
%N A290488 Lower ends of record gaps between numbers that are either prime or twice a prime.
%C A290488 The gap between 31397 and 31454 is due to the record prime gap between 31397 and 31469 being almost exactly twice the record prime gap between 15683 and 15727.
%H A290488 Robert G. Wilson v, <a href="/A290488/b290488.txt">Table of n, a(n) for n = 1..37</a>
%F A290488 a(n) = A290489(n) - A290541(n).
%e A290488 a(3) = 47 because the next number that is a prime or twice a prime after 47 is 53, and that is a record gap of size 6.
%t A290488 nxt[n_] := Block[{k = n +1}, While[ !PrimeQ[ k] && ! PrimeQ[ k/2], k++]; k]; p = 2; q = 3; mx = 0; lst = {}; While[p < 2500000000, If[q > mx + p, mx = q - p; AppendTo[ lst, p]]; p = q; q = nxt@ q]; lst (* _Robert G. Wilson v_, Aug 03 2017 *)
%Y A290488 Cf. A001751, A290489, A290541.
%K A290488 nonn
%O A290488 1,1
%A A290488 _Bobby Jacobs_, Aug 03 2017
%E A290488 a(11) onward from _Robert G. Wilson v_, Aug 03 2017