A152822 Periodic sequence [1,1,0,1] of length 4.
1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1
Offset: 0
Links
- Antti Karttunen, Table of n, a(n) for n = 0..65537
- Index entries for characteristic functions.
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).
Crossrefs
Programs
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Maple
a:= n-> [1,1,0,1][1+irem(n,4)]: seq(a(n), n=0..104); # Alois P. Heinz, Sep 01 2021
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PARI
a(n)=n%4!=2 \\ Jaume Oliver Lafont, Mar 24 2009
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PARI
A152822(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],f[k,2]>1,1)); }; \\ (After multiplicative formula) - Antti Karttunen, May 03 2022
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Python
def A152822(n): return (1,1,0,1)[n&3] # Chai Wah Wu, Jan 10 2023
Formula
a(n) = 3/4 - (1/4)*(-1)^n + (1/2)*cos(n*Pi/2);
a(n+4) = a(n) with a(0) = a(1) = a(3) = 1 and a(2) = 0;
O.g.f.: (1+z+z^3)/(1-z^4);
a(n) = ceiling(cos(Pi*n/4)^2). - Wesley Ivan Hurt, Jun 12 2013
From Antti Karttunen, May 03 2022: (Start)
Multiplicative with a(p^e) = 1 for odd primes, and a(2^e) = [e > 1]. (Here [ ] is the Iverson bracket, i.e., a(2^e) = 0 if e=1, and 1 if e>1).
a(n) = A166486(2+n).
(End)
Dirichlet g.f.: zeta(s)*(1 - 1/2^s + 1/4^s). - Amiram Eldar, Dec 27 2022
Extensions
More terms from Philippe Deléham, Dec 21 2008
Keyword:mult added by Andrew Howroyd, Jul 27 2018