login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A333214 Positions of adjacent unequal terms in the sequence of differences between primes. 23
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 (list; graph; refs; listen; history; text; internal format)
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 * A108473 A298113 A026447

Adjacent sequences:  A333211 A333212 A333213 * A333215 A333216 A333217

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 15 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 30 18:13 EDT 2020. Contains 338090 sequences. (Running on oeis4.)