%I #6 Mar 18 2020 23:02:58
%S 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 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 1,1,2,1,2,2,2,2,2,3,1,3,1,3,3,1,2,2,2
%N Lengths of maximal strictly increasing 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 A333231. The partial sum up to but not including the n-th one is A333382(n).
%e 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 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 A333231 (if its first term is 0).
%Y The strictly decreasing version is A333252.
%Y The equal version is A333254.
%Y Prime gaps are A001223.
%Y Strictly increasing runs of compositions in standard order are A124768.
%Y Positions of strict ascents in the sequence of prime gaps are A258025.
%Y Cf. A000040, A054819, A064113, A084758, A333214, A333230, A333255.
%K nonn
%O 1,1
%A _Gus Wiseman_, Mar 18 2020