A182581 (3-adic valuation of n), read mod 2.

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

Offset

1

Comments

(a(n)) is the unique fixed point of the morphism 0->001, 1->000. This follows by passing from A145204, which gives the positions of 1 in (a(n)), to its complement A007417, and to A014578. - Michel Dekking, Sep 09 2022

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Benoit Cloitre, 10^6 steps of the walk "turn Pi/3 if a(n)=0 and -Pi/3 if a(n)=1".

Dimitri Hendriks, Frits G. W. Dannenberg, Jörg Endrullis, Mark Dow and Jan Willem Klop, Arithmetic Self-Similarity of Infinite Sequences, arXiv preprint 1201.3786 [math.CO], 2012.

Index entries for characteristic functions

Formula

a(n) = A007949(n) mod 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/4. - Amiram Eldar, Jul 24 2022

Mathematica

Mod[IntegerExponent[Range[105], 3], 2] (* Jean-François Alcover, Sep 15 2018 *)

Prog

(PARI) a(n) = valuation(n, 3) % 2; \\ Michel Marcus, Jul 29 2017

Crossrefs

Characteristic function of A145204 \ {0}.

Cf. A007949, A182582.

Binary complement is (A014578(n+1)).

Sequence in context: A309768 A080887 A099395 * A288203 A238470 A286748

Adjacent sequences: A182578 A182579 A182580 * A182582 A182583 A182584

Keyword

nonn

Author

N. J. A. Sloane, May 06 2012

Status

approved