This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333216 #9 Mar 16 2020 12:17:02 %S A333216 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 A333216 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 A333216 14,56,10,26,2,30,65,5,71,12,44,39,37,6,19,47,11,10 %N A333216 Lengths of maximal subsequences without adjacent equal terms in the sequence of prime gaps. %C A333216 Prime gaps are differences between adjacent prime numbers. %C A333216 Essentially the same as A145024. - _R. J. Mathar_, Mar 16 2020 %F A333216 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 A333216 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 A333216 Length/@Split[Differences[Array[Prime,100]],UnsameQ]//Most %Y A333216 First differences of A064113. %Y A333216 The version for the Kolakoski sequence is A306323. %Y A333216 The weakly decreasing version is A333212. %Y A333216 The weakly increasing version is A333215. %Y A333216 The strictly decreasing version is A333252. %Y A333216 The strictly increasing version is A333253. %Y A333216 The equal version is A333254. %Y A333216 Cf. A000040, A001223, A084758, A106356, A124762, A124767, A333214. %K A333216 nonn,hear %O A333216 1,1 %A A333216 _Gus Wiseman_, Mar 15 2020