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A333230 Positions of weak ascents in the sequence of differences between primes.

%I A333230 #5 Mar 18 2020 23:02:39
%S A333230 1,2,3,5,7,8,10,13,14,15,17,20,22,23,26,28,29,31,33,35,36,38,39,41,43,
%T A333230 45,46,49,50,52,54,55,57,60,61,64,65,67,69,70,71,73,75,76,78,79,81,83,
%U A333230 85,86,89,90,93,95,96,98,100,102,104,105,107,109,110,113
%N A333230 Positions of weak ascents in the sequence of differences between primes.
%C A333230 Partial sums of A333252.
%F A333230 Numbers k such that prime(k+2) - 2*prime(k+1) + prime(k) >= 0.
%e A333230 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), ...
%t A333230 Accumulate[Length/@Split[Differences[Array[Prime,100]],#1>#2&]]//Most
%t A333230 - or -
%t A333230 Select[Range[100],Prime[#+1]-Prime[#]<=Prime[#+2]-Prime[#+1]&]
%Y A333230 The version for the Kolakoski sequence is A022297.
%Y A333230 The version for equal differences is A064113.
%Y A333230 The version for strict ascents is A258025.
%Y A333230 The version for strict descents is A258026.
%Y A333230 The version for distinct differences is A333214.
%Y A333230 The version for weak descents is A333231.
%Y A333230 First differences are A333252 (if the first term is 0).
%Y A333230 Prime gaps are A001223.
%Y A333230 Weakly decreasing runs of standard compositions are counted by A124765.
%Y A333230 Weakly increasing runs of standard compositions are counted by A124766.
%Y A333230 Strictly increasing runs of standard compositions are counted by A124768.
%Y A333230 Strictly decreasing runs of standard compositions are counted by A124769.
%Y A333230 Runs of prime gaps with nonzero differences are A333216.
%Y A333230 Cf. A000040, A000720, A036263, A054819, A084758, A333212, A333213, A333215.
%K A333230 nonn
%O A333230 1,2
%A A333230 _Gus Wiseman_, Mar 18 2020