A333230 Positions of weak ascents in the sequence of differences between primes.

1, 2, 3, 5, 7, 8, 10, 13, 14, 15, 17, 20, 22, 23, 26, 28, 29, 31, 33, 35, 36, 38, 39, 41, 43, 45, 46, 49, 50, 52, 54, 55, 57, 60, 61, 64, 65, 67, 69, 70, 71, 73, 75, 76, 78, 79, 81, 83, 85, 86, 89, 90, 93, 95, 96, 98, 100, 102, 104, 105, 107, 109, 110, 113

Offset

1,2

Comments

Partial sums of A333252.

Links

Table of n, a(n) for n=1..64.

Formula

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

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), ...

Mathematica

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

Crossrefs

The version for the Kolakoski sequence is A022297.

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 descents is A333231.

First differences are A333252 (if the first term is 0).

Prime gaps are A001223.

Weakly decreasing runs of standard compositions are counted by A124765.

Weakly increasing runs of standard compositions are counted by A124766.

Strictly increasing runs of standard compositions are counted by A124768.

Strictly decreasing runs of standard compositions are counted by A124769.

Runs of prime gaps with nonzero differences are A333216.

Cf. A000040, A000720, A036263, A054819, A084758, A333212, A333213, A333215.

Sequence in context: A186221 A083027 A060107 * A159556 A219643 A194798

Adjacent sequences: A333227 A333228 A333229 * A333231 A333232 A333233

Keyword

nonn

Author

Gus Wiseman, Mar 18 2020

Status

approved