A338623 a(n) is the length of the longest block of consecutive terms appearing twice (possibly with overlap) among the first n terms of the Thue-Morse sequence (A010060).

0, 0, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

Offset: 1

Author

Rémy Sigrist, Nov 04 2020

Keywords

• nonn

Comments

This sequence is weakly increasing and unbounded (as A010060 is bounded).

Examples

			For n = 8:
- the first 8 terms of A010060 are 0, 1, 1, 0, 1, 0, 0, 1,
- the blocks (0, 1) and (1, 0) are repeated, and there are no length-3 repeated block,
- so a(8) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, PARI program for A338623

Crossrefs

Cf. A010060, A304588, A338624 (Kolakoski variant).

Programs

PARI

See Links section.

Formula

a(n) <= a(n+1) <= a(n) + 1.

a(A304588(n)) = n (and this is the first occurrence of n in the sequence).