A262684 - OEIS

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

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OFFSET

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); };