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

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

Offset: 1

Author

N. J. A. Sloane, Jul 10 2012

Keywords

• nonn

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.

Crossrefs

Cf. A003842, A214216.

Programs

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 *)

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]