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 A333252 #10 Mar 18 2020 23:02:52 %S A333252 1,1,1,2,2,1,2,3,1,1,2,3,2,1,3,2,1,2,2,2,1,2,1,2,2,2,1,3,1,2,2,1,2,3, %T A333252 1,3,1,2,2,1,1,2,2,1,2,1,2,2,2,1,3,1,3,2,1,2,2,2,2,1,2,2,1,3,3,1,1,2, %U A333252 2,1,1,2,3,2,3,2,2,2,2,2,1,3,1,3,1,2,1 %N A333252 Lengths of maximal strictly decreasing subsequences in the sequence of prime gaps (A001223). %C A333252 Prime gaps are differences between adjacent prime numbers. %H A333252 Wikipedia, <a href="https://en.wikipedia.org/wiki/Longest_increasing_subsequence">Longest increasing subsequence</a> %F A333252 Partial sums are A333230. The partial sum up to but not including the n-th one is A333381(n - 1). %e A333252 The prime gaps split into the following strictly decreasing 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), (14,4), (6,2), (10,2), (6), (6,4), (6), ... %t A333252 Length/@Split[Differences[Array[Prime,100]],#1>#2&]//Most %Y A333252 The weakly decreasing version is A333212. %Y A333252 The weakly increasing version is A333215. %Y A333252 The unequal version is A333216. %Y A333252 First differences of A333230 (if the first term is 0). %Y A333252 The strictly increasing version is A333253. %Y A333252 The equal version is A333254. %Y A333252 Prime gaps are A001223. %Y A333252 Strictly decreasing runs of compositions in standard order are A124769. %Y A333252 Positions of strict descents in the sequence of prime gaps are A258026. %Y A333252 Cf. A000040, A064113, A084758, A124764, A124766, A258025, A333213, A333214, A333252, A333256. %K A333252 nonn %O A333252 1,4 %A A333252 _Gus Wiseman_, Mar 18 2020