

A178992


Ordered list in decimal notation of the subwords (with leading zeros omitted) appearing in the infinite Fibonacci word A005614 (0>1 & 1>10).


4



0, 1, 2, 3, 5, 6, 10, 11, 13, 21, 22, 26, 27, 43, 45, 53, 54, 86, 90, 91, 107, 109, 173, 181, 182, 214, 218, 346, 347, 363, 365, 429, 437, 693, 694, 726, 730, 858, 859, 875, 1387, 1389, 1453, 1461, 1717, 1718, 1750, 2774, 2778, 2906, 2907, 2923, 3435, 3437, 3501
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OFFSET

1,3


COMMENTS

The definition mentions the Fibonacci word A005614. Note that the official Fibonacci word is A003849, which would give a different list, namely, the 2'scomplement of the present list.  N. J. A. Sloane, Jan 12 2011


REFERENCES

J.P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1015
T. D. Noe, Table of n, a(n) for n = 1..1652 [The first 1652 terms written in binary, including leading zeros. Not a bfile.]


EXAMPLE

The Fibonacci word has a minimal complexity, i.e., for any n there are n+1 distinct subwords of length n (see for example Allouche and Shallit).
E.g. for n=1 they are '0' and '1', for n=2 '01', '10' and '11' or, in decimal notation '1','2',and '3'.
Some subwords prefixed with '0' have the same decimal value as shorter ones, but there is no real ambiguity as double zeros do not appear in the infinite Fibonacci word.


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]<n+1 && k<Length[f]n, k++]; Length[lst]==n+1, u=Union[u, lst]; n++]; u


CROSSREFS

Cf. A003849, A005614, A171676, A179969.
Sequence in context: A297571 A316503 A316494 * A076474 A324968 A255059
Adjacent sequences: A178989 A178990 A178991 * A178993 A178994 A178995


KEYWORD

nonn,nice,base


AUTHOR

Alexandre Losev, Jan 03 2011


EXTENSIONS

Definition clarified by N. J. A. Sloane, Jan 10 2011


STATUS

approved



