|
%I #9 Mar 16 2020 12:17:02
%S 2,13,21,3,7,8,1,18,29,5,3,8,11,31,4,20,3,7,5,19,21,32,1,19,48,19,29,
%T 32,7,38,1,43,12,33,46,6,16,8,4,34,15,1,19,7,1,23,28,30,22,8,1,7,1,52,
%U 14,56,10,26,2,30,65,5,71,12,44,39,37,6,19,47,11,10
%N Lengths of maximal subsequences without adjacent equal terms in the sequence of prime gaps.
%C Prime gaps are differences between adjacent prime numbers.
%C Essentially the same as A145024. - _R. J. Mathar_, Mar 16 2020
%F Ones correspond to balanced prime quartets (A054800), so the sum of terms up to but not including the n-th one is A000720(A054800(n - 1)) = A090832(n).
%e The prime gaps split into the following subsequences without adjacent equal terms: (1,2), (2,4,2,4,2,4,6,2,6,4,2,4,6), (6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2,10,2,6), (6,4,6), (6,2,10,2,4,2,12), (12,4,2,4,6,2,10,6), ...
%t Length/@Split[Differences[Array[Prime,100]],UnsameQ]//Most
%Y First differences of A064113.
%Y The version for the Kolakoski sequence is A306323.
%Y The weakly decreasing version is A333212.
%Y The weakly increasing version is A333215.
%Y The strictly decreasing version is A333252.
%Y The strictly increasing version is A333253.
%Y The equal version is A333254.
%Y Cf. A000040, A001223, A084758, A106356, A124762, A124767, A333214.
%K nonn,hear
%O 1,1
%A _Gus Wiseman_, Mar 15 2020
|
