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A214217 List of singular subwords (or factors) of the Fibonacci word A003842. 2
2, 11, 212, 11211, 21211212, 1121121211211, 212112121121121211212, 1121121211211212112121121121211211, 2121121211211212112121121121211211212112121121121211212, 11211212112112121121211211212112112121121211211212112121121121211211212112121121121211211 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Complementing the first and last digits of each term gives (essentially) A214216.
LINKS
Kalle Saari, Periods of factors of the Fibonacci word, Department of Mathematics and Turku Centre for Computer Science, University of Turku, 2001 4 Turku, Finland.
Kalle Saari, Periods of factors of the Fibonacci word, in Proceedings of the Sixth International Conference on Words (WORDS’07). Institut de Mathématiques de Luminy (2007) 273-279.
Zhi-Xiong Wen and Zhi-Ying Wen, Some properties of the singular words of the Fibonacci word, European J. Combin. 15 (1994), 587-598.
FORMULA
a(0)=2, a(1)=11, a(2)=212; thereafter a(n)=the concatenation of a(n-2), a(n-3), and a(n-2). [clarified by Harvey P. Dale, May 24 2018]
MATHEMATICA
nxt[{a_, b_, c_}]:={b, c, FromDigits[Join[Flatten[IntegerDigits/@{b, a, b}]]]}; NestList[nxt, {2, 11, 212}, 10][[All, 1]] (* Harvey P. Dale, May 24 2018 *)
CROSSREFS
Sequence in context: A036229 A104337 A283512 * A042805 A088639 A269710
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 10 2012
STATUS
approved

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Last modified July 15 00:37 EDT 2024. Contains 374323 sequences. (Running on oeis4.)