A095111 One minus the parity of 1-fibits in Zeckendorf expansion A014417(n).

1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1

Offset: 0

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn

References

• Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Leonard Rozendaal, Pisano word, tesselation, plane-filling fractal, Preprint, 2017.
• Index entries for characteristic functions.

Crossrefs

Characteristic function of A095096.

Run counts are given by A095276.

Cf. A000045, A003714, A010059, A014417, A095076, A105774.

Programs

Mathematica

1 - Mod[DigitCount[Select[Range[0, 540], BitAnd[#, 2 #] == 0 &], 2, 1], 2] (* Amiram Eldar, Feb 05 2023 *)

Python

def ok(n): return 1 if n==0 else n*(2*n & n == 0)
print([1 - bin(n)[2:].count("1")%2 for n in range(1001) if ok(n)]) # Indranil Ghosh, Jun 08 2017

Formula

a(n) = A010059(A003714(n)).

a(n) = 1 - A095076(n).

a(n) = a'(n+1) where a'(1) = 1 and if n >= 2 with F(k) < n <= F(k+1), a'(n)=1-a'(n-F(k)), where F(k) = A000045(k). E.g., F(5) = 5 < 6 <= F(6) = 8, thus a'(6) = 1 - a'(1) = 0 and a(5) = 0. - Benoit Cloitre, May 10 2005