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

0,1

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.

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

Mathematica

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

Prog

(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

Crossrefs

Characteristic function of A095096.

Run counts are given by A095276.

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

Sequence in context: A267679 A267868 A288733 * A166253 A159638 A187615

Adjacent sequences: A095108 A095109 A095110 * A095112 A095113 A095114

Keyword

nonn

Author

Antti Karttunen, Jun 01 2004

Status

approved