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A152822
Periodic sequence [1,1,0,1] of length 4.
19
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
0,1
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
MAPLE
a:= n-> [1, 1, 0, 1][1+irem(n, 4)]:
seq(a(n), n=0..104); # Alois P. Heinz, Sep 01 2021
PROG
(PARI) a(n)=n%4!=2 \\ Jaume Oliver Lafont, Mar 24 2009
(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
(Python)
def A152822(n): return (1, 1, 0, 1)[n&3] # Chai Wah Wu, Jan 10 2023
CROSSREFS
Characteristic function of A042965.
Cf. A026052, A026064, A320111 (inverse Möbius transform).
Sequence A166486 shifted by two terms.
Sequence in context: A085369 A188082 A046980 * A118831 A118828 A105234
KEYWORD
easy,nonn,mult
AUTHOR
Richard Choulet, Dec 13 2008
EXTENSIONS
More terms from Philippe Deléham, Dec 21 2008
Keyword:mult added by Andrew Howroyd, Jul 27 2018
STATUS
approved