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A080757 First differences of Beatty sequence A022838(n) = floor(n sqrt(3)). 3
1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let S(0) = 1; obtain S(k) from S(k-1) by applying 1 -> 221, 2 -> 2221; sequence is S(0), S(1), S(2), ... - Matthew Vandermast, Mar 25 2003

The sequence (a(n+1)-1) is the homogeneous Sturmian sequence with slope sqrt(3)-1, which is fixed point of the morphism 0->110, 1->1101. So (a(n), n>0) is the unique fixed point of the morphism 1->221, 2->2212. - Michel Dekking, Oct 06 2018

The dual version defined by b(n)=1-(a(n)-1) for n>0 is the Sturmian sequence with slope 1-(sqrt(3)-1) = 2-sqrt(3). It is the fixed point of the morphism 0->0010, 1->001. The sequence (b(n)) prefixed with 0 equals A275855. - Michel Dekking, Oct 06 2018

LINKS

Table of n, a(n) for n=0..105.

Michel Dekking, Substitution invariant Sturmian words and binary trees, Integers 18A, #A7, 1-15 (2018).

Index entries for sequences that are fixed points of mappings

FORMULA

a(n) = A007538(n+1) - 1. - Reinhard Zumkeller, Feb 13 2012

MATHEMATICA

Flatten[ NestList[ Flatten[ # /. {1 -> {2, 2, 1}, 2 -> {2, 2, 2, 1}}] &, {1}, 4]] (* Robert G. Wilson v, Jun 20 2005 *)

Differences[Floor[Range[0, 110]Sqrt[3]]] (* Harvey P. Dale, Mar 15 2018 *)

PROG

(Haskell)

a080757 = (subtract 1) . a007538 . (+ 1)

-- Reinhard Zumkeller, Feb 14 2012

CROSSREFS

Equals A007538(n+1) - 1. Cf. A001030.

Sequence in context: A078377 A291454 A105697 * A037196 A169818 A116543

Adjacent sequences:  A080754 A080755 A080756 * A080758 A080759 A080760

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 25 2003

STATUS

approved

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Last modified November 12 05:52 EST 2019. Contains 329051 sequences. (Running on oeis4.)