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0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) = (5/n), where (k/n) is the Kronecker symbol.
L(1;5) (Dirichlet L-series) is the integral from 0 to 1 of the g.f. of a(n+1). Partial sums are A092202. - Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2010, simplified Jul 27 2010: (Start)
The sequence is the real non-principal Dirichlet character mod 5 (The principal character mod 5 is A011558.)
Associated Dirichlet L-functions are for example L(1,chi) = sum_{n>=1} a(n)/n = A086466 or L(2,chi)= sum_{n>=1} a(n)/n^2 = 0.7062114... = 4*Pi^2/(25*sqrt(5)). (End)
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REFERENCES
| H. Cohn, Advanced Number Theory, Dover Publications, Inc., 1962, p. 173.
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LINKS
| J.-P. Serre, On a theorem of Jordan, Bull. Amer. Math. Soc., 40 (No. 4, 2003), 429-440, see p. 435.
Eric Weisstein's World of Mathematics, Kronecker Symbol
Index entries for two-way infinite sequences
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FORMULA
| If n==0 (mod 5) a(n)=0; if n==1 or 4 (mod 5) a(n)=1; if n==2 or 3 (mod 5) a(n)=-1.
G.f.: x(1-x^2)/(1+x+x^2+x^3+x^4); - Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
G.f.: x(1-x)(1-x^2)/(1-x^5). a(n+5)=a(-n)=a(n).
Euler transform of length 5 sequence [ -1, -1, 0, 0, 1]. - Michael Somos, Jun 17 2005
Transform of the Fibonacci numbers by the Riordan array A102587. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
a(n)=1/5*{n mod 5-2*[(n+1) mod 5]+2*[(n+3) mod 5]-[(n+4) mod 5]} - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 20 2006
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MAPLE
| A080891 := proc(n) numtheory[jacobi](n, 5) ; end proc: seq(A080891(n), n=0..100) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 29 2010]
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PROG
| (PARI) a(n)=kronecker(5, n) [Also, a(n)=kronecker(n, 5) ]
(PARI) a(n)=(n^2+1)%5-1 /* Michael Somos Dec 01 2004 */
(Mupad) numlib::jacobi(n, 5)$ n=0..100 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2008
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CROSSREFS
| Cf. A086937.
Sequence in context: A106743 A011558 A100047 * A112713 A143536 A080110
Adjacent sequences: A080888 A080889 A080890 * A080892 A080893 A080894
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KEYWORD
| sign,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2003
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