A366408 - OEIS

%I #15 Oct 10 2023 09:30:17

%S 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,

%T 53,52,51,50,49,0,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,112,

%U 111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,0,63

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

%C This maximum length is A365624(n).

%C 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.

%H Kevin Ryde, <a href="/A366408/b366408.txt">Table of n, a(n) for n = 1..8192</a>

%H Kevin Ryde, <a href="/A366408/a366408.gp.txt">PARI/GP Code</a>

%e For n=2, the Thue-Morse sequence and the block sought are

%e   t            = 0 1 2 3 4 5 6 7 8

%e   ThueMorse(t) = 0 1 1 0 1 0 0 1 1  (A010060)

%e                          \-------/

%e 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).

%o (PARI) See links.

%Y Cf. A010060, A365624, A005942, A334227.

%K nonn

%O 1,2

%A _Kevin Ryde_, Oct 10 2023