A333252 Lengths of maximal strictly decreasing subsequences in the sequence of prime gaps (A001223).

1, 1, 1, 2, 2, 1, 2, 3, 1, 1, 2, 3, 2, 1, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 3, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 3, 3, 1, 1, 2, 2, 1, 1, 2, 3, 2, 3, 2, 2, 2, 2, 2, 1, 3, 1, 3, 1, 2, 1

Offset: 1

Author

Gus Wiseman, Mar 18 2020

Keywords

• nonn

Comments

Prime gaps are differences between adjacent prime numbers.

Examples

			The prime gaps split into the following strictly 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), (8,4,2), (4,2), (4), (14,4), (6,2), (10,2), (6), (6,4), (6), ...
		

Links

• Wikipedia, Longest increasing subsequence

Crossrefs

The weakly decreasing version is A333212.

The weakly increasing version is A333215.

The unequal version is A333216.

First differences of A333230 (if the first term is 0).

The strictly increasing version is A333253.

The equal version is A333254.

Prime gaps are A001223.

Strictly decreasing runs of compositions in standard order are A124769.

Positions of strict descents in the sequence of prime gaps are A258026.

Cf. A000040, A064113, A084758, A124764, A124766, A258025, A333213, A333214, A333252, A333256.

Programs

Mathematica

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

Formula

Partial sums are A333230. The partial sum up to but not including the n-th one is A333381(n - 1).