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

1,5

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, PARI program for A338623

Formula

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

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A309196 A243283 A243284 * A072613 A029551 A171482

Adjacent sequences: A338620 A338621 A338622 * A338624 A338625 A338626

Keyword

nonn

Author

Rémy Sigrist, Nov 04 2020

Status

approved