A179969 Ordered list in decimal notation of the subwords appearing in the infinite Fibonacci word A005614.

0, 1, 1, 2, 3, 2, 3, 5, 6, 5, 6, 10, 11, 13, 11, 13, 21, 22, 26, 27, 22, 26, 27, 43, 45, 53, 54, 45, 53, 54, 86, 90, 91, 107, 109, 90, 91, 107, 109, 173, 181, 182, 214, 218, 181, 182, 214, 218, 346, 347, 363, 365, 429, 437, 363, 365, 429, 437, 693, 694, 726, 730, 858, 859, 875, 726, 730, 858, 859, 875

Offset: 1

Author

T. D. Noe, Jan 12 2011

Keywords

• nonn
• base

Comments

See A178992 for more details. In binary, the subwords are 0, 1, 01, 10, 11, 010, 011, 101, 110, 0101, 0110, 1010, 1011, 1101,... Converting these numbers to decimal produces this sequence. Except for the initial 0, subwords of the form 0X occur later in the sequence than X. Hence, the second occurrence of a number in this sequence represents the subword having a leading zero. There is a link to a file containing the subwords in binary.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1652
• T. D. Noe, A list of 1652 subwords in binary

Programs

Mathematica

iter=8; f=Nest[Flatten[#/.{0->{1},1->{1,0}}]&,{1},iter]; u={}; n=1; While[lst={}; k=0; While[num=FromDigits[Take[f,{1,n}+k],2]; lst=Union[lst,{num}]; Length[lst]