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A334227 Length of the shortest prefix of the Thue-Morse sequence (A010060) containing, as subwords, all length-n blocks appearing in A010060. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 17:34 EDT 2021. Contains 345418 sequences. (Running on oeis4.)