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 A333231 #5 Mar 18 2020 23:02:46 %S A333231 2,4,6,9,11,12,15,16,18,19,21,24,25,27,30,32,34,36,37,39,40,42,44,46, %T A333231 47,48,51,53,54,55,56,58,59,62,63,66,68,72,73,74,77,80,82,84,87,88,91, %U A333231 92,94,97,99,101,102,103,106,107,108,110,111,112,114,115,118 %N A333231 Positions of weak descents in the sequence of differences between primes. %C A333231 Partial sums of A333253. %F A333231 Numbers k such that prime(k+2) - 2*prime(k+1) + prime(k) >= 0. %e A333231 The prime gaps split into the following strictly increasing subsequences: (1,2), (2,4), (2,4), (2,4,6), (2,6), (4), (2,4,6), (6), (2,6), (4), (2,6), (4,6,8), (4), (2,4), (2,4,14), ... %t A333231 Accumulate[Length/@Split[Differences[Array[Prime,100]],#1<#2&]]//Most %t A333231 - or - %t A333231 Select[Range[100],Prime[#+1]-Prime[#]>=Prime[#+2]-Prime[#+1]&] %Y A333231 The version for the Kolakoski sequence is A025505. %Y A333231 The version for equal differences is A064113. %Y A333231 The version for strict ascents is A258025. %Y A333231 The version for strict descents is A258026. %Y A333231 The version for distinct differences is A333214. %Y A333231 The version for weak ascents is A333230. %Y A333231 First differences are A333253 (if the first term is 0). %Y A333231 Prime gaps are A001223. %Y A333231 Weakly decreasing runs of compositions in standard order are A124765. %Y A333231 Strictly increasing runs of compositions in standard order are A124768. %Y A333231 Runs of prime gaps with nonzero differences are A333216. %Y A333231 Cf. A000040, A000720, A001221, A036263, A054819, A084758, A114994, A124760, A124761, A124766, A124769, A333212. %K A333231 nonn %O A333231 1,1 %A A333231 _Gus Wiseman_, Mar 18 2020