login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)