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

Author

Rémy Sigrist, Dec 23 2021

Keywords

• nonn

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Rémy Sigrist, C program for A350285

Crossrefs

Cf. A010060, A350226.

Programs

C

See Links section.

Formula

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