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

1,1

Comments

Partial sums of A333253.

Links

Table of n, a(n) for n=1..63.

Formula

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

Example

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), ...

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 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.

Sequence in context: A157936 A338348 A184978 * A227132 A024978 A191194

Adjacent sequences: A333228 A333229 A333230 * A333232 A333233 A333234

Keyword

nonn

Author

Gus Wiseman, Mar 18 2020

Status

approved