A262684 - OEIS

%I #16 Oct 01 2018 21:07:50

%S 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,

%T 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,

%U 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

%N Characteristic function for A080218.

%C From _Antti Karttunen_, Oct 01 2018: (Start)

%C 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)

%H Antti Karttunen, <a href="/A262684/b262684.txt">Table of n, a(n) for n = 1..65537</a>

%H Lucilla Baldini, Josef Eschgfäller, <a href="http://arxiv.org/abs/1609.01750">Random functions from coupled dynamical systems</a>, arXiv preprint arXiv:1609.01750 [math.CO], 2016. See Example 3.5.

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

%F Other identities and observations:

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

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

%F a(1) = a(2) = 0; and for n > 2, a(n) = 1-a(A000005(n)). - _Antti Karttunen_, Oct 01 2018

%o (Scheme) (define (A262684 n) (A000035 (A036459 n)))

%o (PARI)

%o up_to = 65537;

%o 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); };

%o v262684 = A262684lista(up_to);

%o A262684(n) = v262684[n]; \\ _Antti Karttunen_, Oct 01 2018

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

%Y Binary complement: A262683.

%K nonn

%O 1

%A _Antti Karttunen_, Sep 28 2015