OFFSET
1,1
COMMENTS
Left shifted sequence is the characteristic function of A035336, and also the second lowest digit of the Zeckendorf expansion of n. - Franklin T. Adams-Watters, Jun 30 2009
a(n) = A188009(n+2), n>=1. - Wolfdieter Lang, Jun 27 2011
Doubling the 0’s in the infinite Fibonacci word A003849 gives (a(n)). - Michel Dekking, Sep 09 2016
This is a morphic sequence, i.e., the letter-to-letter image of the fixed point of a morphism. The fixed point is the unique fixed point A270788 of the three symbol Fibonacci morphism. The letter-to-letter map is 1->0, 2->0, 3->1. - Michel Dekking, May 02 2019
REFERENCES
See references under A000201.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..16384
Michel Dekking and Michael Keane, On the conjugacy class of the Fibonacci dynamical system, arXiv preprint arXiv:1608.04487 [math.DS], 2016.
Michel Dekking and Michael Keane, On the conjugacy class of the Fibonacci dynamical system, Theoretical Computer Science 668 (2017), 59-69.
Jeffrey Shallit and Anatoly Zavyalov, Transduction of Automatic Sequences and Applications, arXiv:2303.15203 [cs.FL], 2023, see p. 31.
FORMULA
a(n) = 1-(1-h(n))-(1-h(n+1)) = h(n)-(1-h(n+1))= h(n)*h(n+1) with h(n):=A005614(n-1), n>=1, the rabbit sequence.
a(n) = A(n+2)-A(n)-3. - Wolfdieter Lang, Jun 27 2011
MATHEMATICA
a[_] = 0; s = Table[n + 2 Floor[n*GoldenRatio], {n, 24}]; Map[Set[a[#], 1] &, s]; Array[a, Max[s]] (* Michael De Vlieger, Mar 29 2023 *)
PROG
(Python)
from math import isqrt
def A123740(n): return (n+2+isqrt(m:=5*(n+2)**2)>>1)-(n+isqrt(m-20*(n+1))>>1)-3 # Chai Wah Wu, Aug 29 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 13 2006
STATUS
approved