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 A290541 #24 Aug 06 2017 23:04:17
%S A290541 1,3,6,10,11,12,13,15,19,21,25,28,35,40,48,57,60,64,70,75,83,90,95,
%T A290541 117,120,144,148,150,153,167,168,196,205,212,214,221,234,244,254,255
%N A290541 Record gaps between numbers that are either prime or twice a prime.
%C A290541 Records in A290496.
%C A290541 The gap of 57 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.
%F A290541 a(n) = A290489(n) - A290488(n).
%e A290541 a(3) = 6 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 A290541 With[{nn = 10^7}, Union@ FoldList[Max, Differences@ #] &@ Union@ Flatten@ {#, 2 TakeWhile[#, # < Prime[nn]/2 &]} &@ Prime@ Range@ nn] (* _Michael De Vlieger_, Aug 06 2017 *)
%Y A290541 Cf. A001751, A290488, A290489, A290496.
%K A290541 more,nonn
%O A290541 1,2
%A A290541 _Bobby Jacobs_, Aug 05 2017
%E A290541 a(36)-a(40) from _Giovanni Resta_, Aug 06 2017