A333215 Lengths of maximal weakly increasing subsequences in the sequence of prime gaps (A001223).

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

Offset

1,1

Comments

Prime gaps are differences between adjacent prime numbers.

Links

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

Formula

Ones correspond to strong prime quartets (A054804), so the sum of terms up to but not including the n-th one is A000720(A054804(n - 1)).

Example

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

Mathematica

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

Crossrefs

Prime gaps are A001223.

Ones correspond to strong prime quartets A054804.

Weakly increasing runs of compositions in standard order are A124766.

First differences of A258026 (with zero prepended).

The version for the Kolakoski sequence is A332875.

The weakly decreasing version is A333212.

The unequal version is A333216.

Positions of weak ascents in prime gaps are A333230.

The strictly decreasing version is A333252.

The strictly increasing version is A333253.

The equal version is A333254.

Cf. A000040, A000720, A036263, A054819, A064113, A084758, A124765, A124768, A258025, A333213, A333214.

Sequence in context: A304786 A335381 A018845 * A028947 A068152 A278970

Adjacent sequences: A333212 A333213 A333214 * A333216 A333217 A333218

Keyword

nonn

Author

Gus Wiseman, Mar 14 2020

Status

approved