

A214217


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


2



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

1,1


COMMENTS

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


REFERENCES

Kalle Saari, Periods of factors of the Fibonacci word, Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland (2001), citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.992
K. Saari, Periods of factors of the Fibonacci word, in Proceedings of the Sixth International Conference on Words (WORDSâ€™07). Institut de MathĂ©matiques de Luminy (2007) 273279.
Wen, Z.X.; Wen, Z.Y. Some properties of the singular words of the Fibonacci word, European J. Combin. 15 (1994), 587598.


LINKS

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


FORMULA

a(0)=2, a(1)=11, a(2)=212; thereafter a(n)=the concatenation of a(n2), a(n3), and a(n2).


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


EXTENSIONS

Formula clarified by Harvey P. Dale, May 24 2018


STATUS

approved



