A333214 Positions of adjacent unequal terms in the sequence of differences between primes.

1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Formula

Numbers k such that prime(k+1) - prime(k) != prime(k+2) - prime(k+1).

Example

The sequence of differences between primes splits into the following runs: (1), (2,2), (4), (2), (4), (2), (4), (6), (2), (6), (4), (2), (4), (6,6), (2), (6), (4), (2), (6), (4), (6).

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 A054353.

Complement of A064113 (the version for adjacent equal terms).

Runs of compositions in standard order are counted by A124767.

A triangle for runs of compositions is A238279.

The version for strict ascents is A258025.

The version for strict descents is A258026.

The version for weak ascents is A333230.

The version for weak descents is A333231.

First differences are A333254 (if the first term is 0).

Cf. A000040, A001223, A084758, A106356, A124762, A333216, A333490, A333491.

Sequence in context: A132147 A118955 A191838 * A363768 A108473 A298113

Adjacent sequences: A333211 A333212 A333213 * A333215 A333216 A333217

Keyword

nonn

Author

Gus Wiseman, Mar 15 2020

Status

approved