A214217 List of singular subwords (or factors) of the Fibonacci word A003842.

2, 11, 212, 11211, 21211212, 1121121211211, 212112121121121211212, 1121121211211212112121121121211211, 2121121211211212112121121121211211212112121121121211212, 11211212112112121121211211212112112121121211211212112121121121211211212112121121121211211

Offset

1,1

Comments

Complementing the first and last digits of each term gives (essentially) A214216.

Links

Table of n, a(n) for n=1..10.

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

Cf. A003842, A214216.

Sequence in context: A036229 A104337 A283512 * A042805 A088639 A269710

Adjacent sequences: A214214 A214215 A214216 * A214218 A214219 A214220

Keyword

nonn

Author

N. J. A. Sloane, Jul 10 2012

Status

approved