A334227 Length of the shortest prefix of the Thue-Morse sequence (A010060) containing, as subwords, all length-n blocks appearing in A010060.

0, 2, 7, 8, 15, 16, 29, 30, 31, 32, 57, 58, 59, 60, 61, 62, 63, 64, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246

Offset

0,2

Links

Table of n, a(n) for n=0..55.

Formula

a(0) = 0, a(1) = 2, a(2) = 2, and a(2^i + j) = 7*2^i + j-1 for i >= 0 and 2 <= j <= 2^i + 1.

Example

For n = 3 the length-8 prefix 01101001 contains all length-3 subwords appearing in Thue-Morse, namely, {011,110,101,010,100,001}, and no shorter prefix works.

Prog

(PARI) a(n)=if(n<3, [0, 2, 7][n+1], my(i=exponent(n), N=1<<i, j=n-N); if(j<2, N>>=1; j=n-N); 7*N+j-1) \\ Charles R Greathouse IV, Apr 30 2020

Crossrefs

Cf. A010060.

Sequence in context: A063729 A299151 A023178 * A080572 A263602 A162664

Adjacent sequences: A334224 A334225 A334226 * A334228 A334229 A334230

Keyword

nonn,easy

Author

Jeffrey Shallit, Apr 19 2020

Status

approved