A333212 Lengths of maximal weakly decreasing subsequences in the sequence of prime gaps (A001223).

1, 2, 2, 2, 1, 2, 3, 1, 3, 3, 2, 1, 3, 2, 1, 2, 2, 2, 3, 3, 2, 2, 4, 1, 2, 5, 3, 1, 3, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 1, 2, 2, 4, 1, 4, 4, 3, 1, 3, 2, 1, 1, 2, 5, 3, 2, 2, 2, 2, 2, 1, 3, 1, 3, 1, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 3

Offset: 1

Author

Gus Wiseman, Mar 14 2020

Keywords

• nonn

Comments

Prime gaps are differences between adjacent prime numbers.

Examples

			The prime gaps split into the following weakly 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), ...
		

Crossrefs

First differences of A258025 (with zero prepended).

The version for the Kolakoski sequence is A332273.

The weakly increasing version is A333215.

The unequal version is A333216.

The strictly decreasing version is A333252.

The strictly increasing version is A333253.

The equal version is A333254.

Prime gaps are A001223.

Positions of adjacent equal differences are A064113.

Weakly decreasing runs of compositions in standard order are A124765.

Positions of strict ascents in the sequence of prime gaps are A258025.

Cf. A000040, A000720, A001221, A036263, A054819, A084758, A114994, A124760, A124761, A124768, A333213, A333214.

Programs

Mathematica

Length/@Split[Differences[Array[Prime,100]],#1>=#2&]//Most

Formula

Ones correspond to weak prime quartets A054819, so the sum of terms up to but not including the n-th one is A000720(A054819(n - 1)).