A350285 a(n) is the least d > 0 such that A010060(n) = A010060(n - i*d) for i = 0..A350226(n)-1 (A010060 corresponds to the Thue-Morse sequence).

1, 1, 1, 3, 2, 2, 3, 3, 1, 3, 5, 3, 3, 6, 3, 3, 2, 7, 3, 6, 5, 5, 3, 3, 6, 3, 5, 9, 3, 6, 6, 3, 1, 3, 5, 7, 6, 6, 12, 3, 10, 10, 7, 7, 3, 9, 3, 3, 12, 7, 3, 6, 5, 10, 9, 17, 7, 6, 5, 9, 3, 12, 6, 9, 2, 7, 3, 15, 5, 5, 14, 14, 9, 12, 12, 12, 3, 19, 6, 3, 17, 20

Offset

0,4

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, C program for A350285

Formula

a(n) * (A350226(n) - 1) <= n.

Example

For n = 21:
- A350226(21) = 3,
- the first 22 terms of A010060 are:
       0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1
                                        *              *              *
                            *                    *                    *
          *                             *                             *
- A010060(11) = A010060(16) = A010060(21),
- A010060(7) = A010060(14) = A010060(21),
- A010060(1) = A010060(11) = A010060(21),
- the first differences are 5, 7 and 10,
- the least first difference is 5,
- so a(21) = 5.

Prog

(C) See Links section.

Crossrefs

Cf. A010060, A350226.

Sequence in context: A294299 A125504 A243929 * A347381 A075392 A069901

Adjacent sequences: A350282 A350283 A350284 * A350286 A350287 A350288

Keyword

nonn

Author

Rémy Sigrist, Dec 23 2021

Status

approved