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%I #5 Mar 18 2020 23:02:46
%S 2,4,6,9,11,12,15,16,18,19,21,24,25,27,30,32,34,36,37,39,40,42,44,46,
%T 47,48,51,53,54,55,56,58,59,62,63,66,68,72,73,74,77,80,82,84,87,88,91,
%U 92,94,97,99,101,102,103,106,107,108,110,111,112,114,115,118
%N Positions of weak descents in the sequence of differences between primes.
%C Partial sums of A333253.
%F Numbers k such that prime(k+2) - 2*prime(k+1) + prime(k) >= 0.
%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 Accumulate[Length/@Split[Differences[Array[Prime,100]],#1<#2&]]//Most
%t - or -
%t Select[Range[100],Prime[#+1]-Prime[#]>=Prime[#+2]-Prime[#+1]&]
%Y The version for the Kolakoski sequence is A025505.
%Y The version for equal differences is A064113.
%Y The version for strict ascents is A258025.
%Y The version for strict descents is A258026.
%Y The version for distinct differences is A333214.
%Y The version for weak ascents is A333230.
%Y First differences are A333253 (if the first term is 0).
%Y Prime gaps are A001223.
%Y Weakly decreasing runs of compositions in standard order are A124765.
%Y Strictly increasing runs of compositions in standard order are A124768.
%Y Runs of prime gaps with nonzero differences are A333216.
%Y Cf. A000040, A000720, A001221, A036263, A054819, A084758, A114994, A124760, A124761, A124766, A124769, A333212.
%K nonn
%O 1,1
%A _Gus Wiseman_, Mar 18 2020