A333216 Lengths of maximal subsequences without adjacent equal terms in the sequence of prime gaps.

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, 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, 14, 56, 10, 26, 2, 30, 65, 5, 71, 12, 44, 39, 37, 6, 19, 47, 11, 10

Offset: 1

Author

Gus Wiseman, Mar 15 2020

Keywords

• nonn
• hear

Comments

Prime gaps are differences between adjacent prime numbers.

Essentially the same as A145024. - R. J. Mathar, Mar 16 2020

Examples

			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), ...
		

Crossrefs

First differences of A064113.

The version for the Kolakoski sequence is A306323.

The weakly decreasing version is A333212.

The weakly increasing version is A333215.

The strictly decreasing version is A333252.

The strictly increasing version is A333253.

The equal version is A333254.

Cf. A000040, A001223, A084758, A106356, A124762, A124767, A333214.

Programs

Mathematica

Length/@Split[Differences[Array[Prime,100]],UnsameQ]//Most

Formula

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).