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A011558
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Expansion of (x+x^3)/(1+x+...+x^4) mod 2.
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17
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Multiplicative with a(5^e) = 0, a(p^e) = 1 otherwise. David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009: (Start)
a(n)=1-A079998(n); characteristic function of numbers coprime to 5; a(A047201(n))=1; a(A008587(n))=0;
A033437(n) = SUM(a(k)*(n-k): 0<=k<=n). (End)
Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2010: (Start)
The sequence is the principal Dirichlet character mod 5 (The other real character mod 5 is A080891.)
Associated Dirichlet L-functions are for example L(2,chi)= sum_{n>=1} a(n)/n^2 = 1.5791367... = (psi'(1/5)+psi'(2/5)+psi'(3/5)+psi'(4/5))/25 or L(3,chi)= sum_{n>=1} a(n)/n^3 = 1.192440... = -(psi''(1/5)+psi''(2/5)+psi''(3/5)+psi''(4/5))/250, where psi' and psi'' are the trigamma and tetragamma functions. (End)
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REFERENCES
| R. Gold, Characteristic linear sequences and their coset functions, J. SIAM Applied. Math., 14 (1966), 980-985.
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LINKS
| Michael Gilleland, Some Self-Similar Integer Sequences
Index entries for characteristic functions [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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FORMULA
| O.g.f.: x*(1+x+x^2+x^3)/(1-x^5). [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 05 2009]
a(n)=(1/8)*{3*(n mod 4)+[(n+1) mod 4]+[(n+2) mod 4]-[(n+3) mod 4]}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Feb 11 2009]
a(n)=n^4 mod 5 [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 20 2010]
Sum_{n=1..infinity} a(n)/n^s = L(s,chi) = (1-1/5^s)*Riemann_zeta(s), s>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2010]
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MAPLE
| seq(n^4 mod 5, n=0..50); [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 20 2010]
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MATHEMATICA
| Mod[#, 2]&/@CoefficientList[Series[(x+x^3)/(1+x+x^2+x^3+x^4) , {x, 0, 100}], x] (* or *) Flatten[Table[{0, 1, 1, 1, 1}, {30}]] (* From Harvey P. Dale, May 15 2011 *)
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CROSSREFS
| Cf. A000035, A011655, A109720 coprimality with 2, 3, 7, respectively. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 05 2009]
Cf. A168185, A145568, A168184, A168182, A168181, A097325, A166486. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
Sequence in context: A069513 A092248 A106743 * A100047 A080891 A112713
Adjacent sequences: A011555 A011556 A011557 * A011559 A011560 A011561
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KEYWORD
| nonn,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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