A333231 Positions of weak descents in the sequence of differences between primes.

2, 4, 6, 9, 11, 12, 15, 16, 18, 19, 21, 24, 25, 27, 30, 32, 34, 36, 37, 39, 40, 42, 44, 46, 47, 48, 51, 53, 54, 55, 56, 58, 59, 62, 63, 66, 68, 72, 73, 74, 77, 80, 82, 84, 87, 88, 91, 92, 94, 97, 99, 101, 102, 103, 106, 107, 108, 110, 111, 112, 114, 115, 118

Offset: 1

Author

Gus Wiseman, Mar 18 2020

Keywords

• nonn

Comments

Partial sums of A333253.

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), ...
		

Crossrefs

The version for the Kolakoski sequence is A025505.

The version for equal differences is A064113.

The version for strict ascents is A258025.

The version for strict descents is A258026.

The version for distinct differences is A333214.

The version for weak ascents is A333230.

First differences are A333253 (if the first term is 0).

Prime gaps are A001223.

Weakly decreasing runs of compositions in standard order are A124765.

Strictly increasing runs of compositions in standard order are A124768.

Runs of prime gaps with nonzero differences are A333216.

Cf. A000040, A000720, A001221, A036263, A054819, A084758, A114994, A124760, A124761, A124766, A124769, A333212.

Programs

Mathematica

Accumulate[Length/@Split[Differences[Array[Prime,100]],#1<#2&]]//Most
- or -
Select[Range[100],Prime[#+1]-Prime[#]>=Prime[#+2]-Prime[#+1]&]

Formula

Numbers k such that prime(k+2) - 2*prime(k+1) + prime(k) >= 0.