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 A333253 #6 Mar 18 2020 23:02:58 %S A333253 2,2,2,3,2,1,3,1,2,1,2,3,1,2,3,2,2,2,1,2,1,2,2,2,1,1,3,2,1,1,1,2,1,3, %T A333253 1,3,2,4,1,1,3,3,2,2,3,1,3,1,2,3,2,2,1,1,3,1,1,2,1,1,2,1,3,1,2,4,2,1, %U A333253 1,1,2,1,2,2,2,2,2,3,1,3,1,3,3,1,2,2,2 %N A333253 Lengths of maximal strictly increasing subsequences in the sequence of prime gaps (A001223). %C A333253 Prime gaps are differences between adjacent prime numbers. %H A333253 Wikipedia, <a href="https://en.wikipedia.org/wiki/Longest_increasing_subsequence">Longest increasing subsequence</a> %F A333253 Partial sums are A333231. The partial sum up to but not including the n-th one is A333382(n). %e A333253 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 A333253 Length/@Split[Differences[Array[Prime,100]],#1<#2&]//Most %Y A333253 The weakly decreasing version is A333212. %Y A333253 The weakly increasing version is A333215. %Y A333253 The unequal version is A333216. %Y A333253 First differences of A333231 (if its first term is 0). %Y A333253 The strictly decreasing version is A333252. %Y A333253 The equal version is A333254. %Y A333253 Prime gaps are A001223. %Y A333253 Strictly increasing runs of compositions in standard order are A124768. %Y A333253 Positions of strict ascents in the sequence of prime gaps are A258025. %Y A333253 Cf. A000040, A054819, A064113, A084758, A333214, A333230, A333255. %K A333253 nonn %O A333253 1,1 %A A333253 _Gus Wiseman_, Mar 18 2020