A279620 Limit of the sequence of words defined by w(1) = 1, w(2) = 1221, and w(n) = w(n-1) 2 w(n-2) 2 w(n-1) for n >= 2. Also the fixed point of the map 1 -> 122, 2 -> 12.

1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2

Offset

1,2

References

Allombert, Bill, Nicolas Brisebarre, and Alain Lasjaunias. "On a two-valued sequence and related continued fractions in power series fields." The Ramanujan Journal 45.3 (2018): 859-871. See W in Theorem 2.

Links

Table of n, a(n) for n=1..130.

Alain Lasjaunias and Jia-Yan Yao, Hyperquadratic continued fractions and automatic sequences, Finite Fields and Their Applications 40 (2016) 46-60. See Section 4.

Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003. Apparently unpublished. This is a scanned copy of the version that the author sent to me in 2003. The sequence is on page 1, but there is a typo in the definition: g(1)=112 should be g(1)=122.

Mathematica

Nest[Flatten[#]/.{1->{1, 2, 2}, 2->{1, 2}}&, {1}, 6]//Flatten (* Harvey P. Dale, Apr 21 2020 *)

Crossrefs

Equals A189687(n) + 1.

For runs, see A318930.

For w(n) see A328991.

Sequence in context: A138702 A344339 A348364 * A278109 A216665 A301384

Adjacent sequences: A279617 A279618 A279619 * A279621 A279622 A279623

Keyword

nonn

Author

Jeffrey Shallit, Dec 21 2016

Status

approved