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

Author

Jeffrey Shallit, Apr 19 2020

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

Cf. A010060.

Programs

PARI

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

Formula

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