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

1,4

Comments

Prime gaps are differences between adjacent prime numbers.

Links

Table of n, a(n) for n=1..87.

Wikipedia, Longest increasing subsequence

Formula

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

Example

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), ...

Mathematica

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

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.

Sequence in context: A307219 A345764 A236573 * A366376 A293375 A232174

Adjacent sequences: A333249 A333250 A333251 * A333253 A333254 A333255

Keyword

nonn

Author

Gus Wiseman, Mar 18 2020

Status

approved