A262684 Characteristic function for A080218.

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

Offset

1

Comments

From Antti Karttunen, Oct 01 2018: (Start)

From n=2 onward this is also binary sequence mentioned in Baldini & Eschgfäller 2016 paper that is generated by a coupled dynamical system (f,lambda,alpha) with parameters set as f(k) = A000005(k), lambda(y) = 1-y for y in Y = {0,1}, and alpha(k) = 0 for k in Omega = {2}. Then a(n) for n >= 2 is defined by a(n) = alpha(n) if n in Omega, and otherwise by a(n) = lambda(a(f(n))), which simplifies to the formula I have today added to the formula section. (End)

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Lucilla Baldini, Josef Eschgfäller, Random functions from coupled dynamical systems, arXiv preprint arXiv:1609.01750 [math.CO], 2016. See Example 3.5.

Index entries for characteristic functions

Formula

a(n) = A000035(A036459(n)).

Other identities and observations:

For all n >= 1, a(n) = 1 - A262683(n).

For n > 2, if A010051(n) = 1, then a(n) = 1. [For all odd primes the sequence is 1.]

a(1) = a(2) = 0; and for n > 2, a(n) = 1-a(A000005(n)). - Antti Karttunen, Oct 01 2018

Prog

(Scheme) (define (A262684 n) (A000035 (A036459 n)))
(PARI)
up_to = 65537;
A262684lista(up_to) = { my(v=vector(up_to)); v[1] = v[2] = 0; for(n=3, up_to, v[n] = 1-v[numdiv(n)]); (v); };
v262684 = A262684lista(up_to);
A262684(n) = v262684[n]; \\ Antti Karttunen, Oct 01 2018

Crossrefs

Cf. A000005, A000035, A010051, A036459, A049820, A080218, A291291, A291293.

Binary complement: A262683.

Sequence in context: A043545 A094754 A321694 * A287382 A074290 A091225

Adjacent sequences: A262681 A262682 A262683 * A262685 A262686 A262687

Keyword

nonn

Author

Antti Karttunen, Sep 28 2015

Status

approved