A338626 a(n) is the least k such that the first k terms of the Kolakoski sequence (A000002) contain a length-n repeated block.

3, 6, 9, 10, 13, 15, 16, 28, 32, 33, 40, 41, 42, 43, 69, 70, 71, 72, 94, 95, 96, 97, 98, 99, 106, 107, 108, 109, 214, 215, 216, 217, 218, 219, 220, 221, 222, 297, 298, 299, 300, 301, 339, 340, 487, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730

Offset

1,1

Comments

The sequence contains large runs of consecutive integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..9511 (terms < 3000000)

Rémy Sigrist, PARI program for A338626

Rémy Sigrist, Perl program for A338626

Formula

A338624(a(n)) = n.

Example

For n = 2:
- the first 5 terms of Kolakoski sequence are: 1, 2, 2, 1, 1,
- they have no length-2 repeated block,
- the first 6 terms of Kolakoski sequence are: 1, 2, 2, 1, 1, 2,
- they have a length-2 repeated block: 1, 2,
- so a(2) = 6.

Prog

(PARI) See Links section.
(Perl) See Links section.

Crossrefs

Cf. A000002, A304588 (Thue-Morse variant), A338624.

Sequence in context: A363950 A268328 A247575 * A289130 A188299 A187577

Adjacent sequences: A338623 A338624 A338625 * A338627 A338628 A338629

Keyword

nonn

Author

Rémy Sigrist, Nov 04 2020

Status

approved