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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
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
Lucilla Baldini, Josef Eschgfäller, Random functions from coupled dynamical systems, arXiv preprint arXiv:1609.01750 [math.CO], 2016. See Example 3.5.
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
Binary complement: A262683.
Sequence in context: A043545 A094754 A321694 * A373263 A287382 A074290
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 28 2015
STATUS
approved