|
%I #10 May 16 2020 19:35:14
%S 1,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,
%T 28,29,30,31,32,33,34,35,37,38,40,41,42,43,44,45,47,48,49,50,51,52,53,
%U 56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,74,75
%N Positions of adjacent unequal terms in the sequence of differences between primes.
%F Numbers k such that prime(k+1) - prime(k) != prime(k+2) - prime(k+1).
%e The sequence of differences between primes splits into the following runs: (1), (2,2), (4), (2), (4), (2), (4), (6), (2), (6), (4), (2), (4), (6,6), (2), (6), (4), (2), (6), (4), (6).
%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 A054353.
%Y Complement of A064113 (the version for adjacent equal terms).
%Y Runs of compositions in standard order are counted by A124767.
%Y A triangle for runs of compositions is A238279.
%Y The version for strict ascents is A258025.
%Y The version for strict descents is A258026.
%Y The version for weak ascents is A333230.
%Y The version for weak descents is A333231.
%Y First differences are A333254 (if the first term is 0).
%Y Cf. A000040, A001223, A084758, A106356, A124762, A333216, A333490, A333491.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 15 2020
|
