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 A333212 #13 Mar 29 2020 00:58:27 %S A333212 1,2,2,2,1,2,3,1,3,3,2,1,3,2,1,2,2,2,3,3,2,2,4,1,2,5,3,1,3,1,2,2,1,1, %T A333212 4,1,2,1,2,2,2,1,3,1,3,2,1,2,2,4,1,4,4,3,1,3,2,1,1,2,5,3,2,2,2,2,2,1, %U A333212 3,1,3,1,2,1,3,2,2,2,2,2,2,2,1,2,2,1,3 %N A333212 Lengths of maximal weakly decreasing subsequences in the sequence of prime gaps (A001223). %C A333212 Prime gaps are differences between adjacent prime numbers. %F A333212 Ones correspond to weak prime quartets A054819, so the sum of terms up to but not including the n-th one is A000720(A054819(n - 1)). %e A333212 The prime gaps split into the following weakly 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), ... %t A333212 Length/@Split[Differences[Array[Prime,100]],#1>=#2&]//Most %Y A333212 First differences of A258025 (with zero prepended). %Y A333212 The version for the Kolakoski sequence is A332273. %Y A333212 The weakly increasing version is A333215. %Y A333212 The unequal version is A333216. %Y A333212 The strictly decreasing version is A333252. %Y A333212 The strictly increasing version is A333253. %Y A333212 The equal version is A333254. %Y A333212 Prime gaps are A001223. %Y A333212 Positions of adjacent equal differences are A064113. %Y A333212 Weakly decreasing runs of compositions in standard order are A124765. %Y A333212 Positions of strict ascents in the sequence of prime gaps are A258025. %Y A333212 Cf. A000040, A000720, A001221, A036263, A054819, A084758, A114994, A124760, A124761, A124768, A333213, A333214. %K A333212 nonn %O A333212 1,2 %A A333212 _Gus Wiseman_, Mar 14 2020