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A152822
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Periodic sequence [1,1,0,1] of length 4.
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6
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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
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OFFSET
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0,1
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LINKS
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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).
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FORMULA
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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);
From Paolo P. Lava, Dec 15 2008: (Start)
a(n) = (1/8)*((n mod 4) - ((n+1) mod 4) + 3*((n+2) mod 4)((n+3) mod 4)), with n >= 0.
a(n) = (1/4)*(3 + i^n + (-i)^n - (-1)^n), with n >= 0 and i = sqrt(-1). (End)
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)
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MAPLE
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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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PROG
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(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
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CROSSREFS
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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
Adjacent sequences: A152819 A152820 A152821 * A152823 A152824 A152825
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KEYWORD
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easy,nonn,mult
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AUTHOR
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Richard Choulet, Dec 13 2008
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EXTENSIONS
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More terms from Philippe Deléham, Dec 21 2008
Keyword:mult added by Andrew Howroyd, Jul 27 2018
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STATUS
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approved
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