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A262684 Characteristic function for A080218. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 03:22 EDT 2020. Contains 337291 sequences. (Running on oeis4.)