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 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 (list; graph; refs; listen; history; text; internal format)
 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's-complement 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 b-file.] 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]

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Last modified April 20 06:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)