A366408 Starting index in the Thue-Morse sequence (A010060) of the first maximum length block in which every subword of length n is distinct.

0, 4, 0, 7, 0, 3, 14, 13, 0, 7, 6, 5, 28, 27, 26, 25, 0, 15, 14, 13, 12, 11, 10, 9, 56, 55, 54, 53, 52, 51, 50, 49, 0, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 0, 63

Offset: 1

Author

Kevin Ryde, Oct 10 2023

Keywords

• nonn

Comments

This maximum length is A365624(n).

For n=1 and n = 2^k + 1 >= 3, a(n) = 0 since in those cases A005942(n) + n-1 = A334227(n) shows the Thue-Morse sequence starts with all possible subwords of length n without duplication.

Examples

			For n=2, the Thue-Morse sequence and the block sought are
  t            = 0 1 2 3 4 5 6 7 8
  ThueMorse(t) = 0 1 1 0 1 0 0 1 1  (A010060)
                         \-------/
In the block of terms starting at t = a(2) = 4 and length A365624(2) = 5, every subword of length n=2 is distinct (10, 00, 01, 11).
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..8192
• Kevin Ryde, PARI/GP Code

Crossrefs

Cf. A010060, A365624, A005942, A334227.

Programs

PARI

\\ See links.