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