A333253 Lengths of maximal strictly increasing subsequences in the sequence of prime gaps (A001223).

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

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 increasing 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), ...
		

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 A333231 (if its first term is 0).

The strictly decreasing version is A333252.

The equal version is A333254.

Prime gaps are A001223.

Strictly increasing runs of compositions in standard order are A124768.

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

Cf. A000040, A054819, A064113, A084758, A333214, A333230, A333255.

Programs

Mathematica

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

Formula

Partial sums are A333231. The partial sum up to but not including the n-th one is A333382(n).