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%I #13 Mar 29 2020 00:58:27
%S 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 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 3,1,3,1,2,1,3,2,2,2,2,2,2,2,1,2,2,1,3
%N Lengths of maximal weakly decreasing subsequences in the sequence of prime gaps (A001223).
%C Prime gaps are differences between adjacent prime numbers.
%F 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 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 Length/@Split[Differences[Array[Prime,100]],#1>=#2&]//Most
%Y First differences of A258025 (with zero prepended).
%Y The version for the Kolakoski sequence is A332273.
%Y The weakly increasing version is A333215.
%Y The unequal version is A333216.
%Y The strictly decreasing version is A333252.
%Y The strictly increasing version is A333253.
%Y The equal version is A333254.
%Y Prime gaps are A001223.
%Y Positions of adjacent equal differences are A064113.
%Y Weakly decreasing runs of compositions in standard order are A124765.
%Y Positions of strict ascents in the sequence of prime gaps are A258025.
%Y Cf. A000040, A000720, A001221, A036263, A054819, A084758, A114994, A124760, A124761, A124768, A333213, A333214.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 14 2020
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