A092436 a(n) = 1/2 + (-1)^n*(1/2 - A010060(floor(n/2))).

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

Offset: 1

Author

Benoit Cloitre, Mar 23 2004

Keywords

• nonn

Comments

From Jeffrey Shallit, Mar 02 2022: (Start)

Also, the parity of the number of 2's in the bijective base-2 representation of n - 1; this is the base-2 representation using the digits {1,2} in place of {0,1}.

Also, solution of the equation a = 0 mu(a), where mu is the Thue-Morse morphism 0 -> 01, 1 -> 10. (End)

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027914, A010060.

Programs

Mathematica

Flatten[ NestList[ Function[l, {Flatten[(l /. {0 -> {0, 1}, 1 -> {1, 0}})]}], {0}, 6]] (* Robert G. Wilson v, May 19 2005 *)

Python

def A092436(n): return n.bit_count()&1^1 # Chai Wah Wu, Mar 03 2023

Formula

a(n) = 1-A010060(n). - Chai Wah Wu, Mar 03 2023