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A097325
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Periodic sequence 0,1,1,1,1,1...
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13
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0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) is 0 if 6 divides n, 1 otherwise.
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009: (Start)
a(n)=1-A079979(n); a(A047253(n))=1; a(A008588(n))=0;
A033438(n) = SUM(a(k)*(n-k): 0<=k<=n). (End)
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LINKS
| Index entries for characteristic functions [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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FORMULA
| G.f.: 1/(1-x) - 1/(1-x^6) = Sum[k>=0, x^k - x^(6k)].
Recurrence: a(n+6) = a(n), a(0) = 0, a(i) = 1, 1 <= i <= 5.
a(n) = (1/4) * {3 - (-1)^n - (-1)^[(n+1)/3] - (-1)^[(2n+1)/3]}.
a(n)={[(1/3)*(cos(2*n*Pi/3)+1/2)*(1+(-1)^n)]-1}^2 - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 09 2006
Dirichlet g.f. (1-1/6^s)*zeta(s). - R. J. Mathar, Feb 19 2011
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PROG
| (PARI) a(n) = sign(n%6)
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CROSSREFS
| Characteristic sequence of A047253. Binary complement of A079979.
Cf. A168185, A145568, A168184, A168182, A168181, A109720, A011558, A166486, A011655, A000035. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
Sequence in context: A143536 A080110 A122895 * A167393 A106549 A075897
Adjacent sequences: A097322 A097323 A097324 * A097326 A097327 A097328
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KEYWORD
| nonn,easy
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AUTHOR
| Ralf Stephan, Aug 16 2004
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