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 A333215 #9 Mar 15 2020 22:25:30 %S A333215 4,2,3,2,1,4,2,1,2,3,1,2,3,2,2,3,3,2,2,3,1,3,2,3,2,1,3,1,3,2,4,2,3,3, %T A333215 2,2,3,1,3,1,2,3,2,2,2,3,2,3,1,2,1,4,2,4,2,1,2,2,1,2,2,2,2,2,3,1,3,1, %U A333215 3,3,1,4,4,2,2,2,3,2,3,1,5,3,2,2,4,3,3 %N A333215 Lengths of maximal weakly increasing subsequences in the sequence of prime gaps (A001223). %C A333215 Prime gaps are differences between adjacent prime numbers. %F A333215 Ones correspond to strong prime quartets (A054804), so the sum of terms up to but not including the n-th one is A000720(A054804(n - 1)). %e A333215 The prime gaps split into the following weakly 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 A333215 Length/@Split[Differences[Array[Prime,100]],#1<=#2&]//Most %Y A333215 Prime gaps are A001223. %Y A333215 Ones correspond to strong prime quartets A054804. %Y A333215 Weakly increasing runs of compositions in standard order are A124766. %Y A333215 First differences of A258026 (with zero prepended). %Y A333215 The version for the Kolakoski sequence is A332875. %Y A333215 The weakly decreasing version is A333212. %Y A333215 The unequal version is A333216. %Y A333215 Positions of weak ascents in prime gaps are A333230. %Y A333215 The strictly decreasing version is A333252. %Y A333215 The strictly increasing version is A333253. %Y A333215 The equal version is A333254. %Y A333215 Cf. A000040, A000720, A036263, A054819, A064113, A084758, A124765, A124768, A258025, A333213, A333214. %K A333215 nonn %O A333215 1,1 %A A333215 _Gus Wiseman_, Mar 14 2020