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

Author

Rémy Sigrist, Nov 04 2020

Keywords

• nonn

Comments

The sequence contains large runs of consecutive integers.

Examples

			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.
		

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

Crossrefs

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

Programs

PARI

See Links section.

Perl

See Links section.

Formula

A338624(a(n)) = n.