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3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1
(list;
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OFFSET
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0,1
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COMMENTS
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For n>1: a(n) = GCD of the n-th and (n+2)-th triangular numbers = A050873(A000217(n+2),A000217(n)). - Reinhard Zumkeller, May 28 2007
Contribution from Klaus Brockhaus, May 24 2010: (Start)
Continued fraction expansion of (3+sqrt(17))/2.
Decimal expansion of 311/999. (End)
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LINKS
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Table of n, a(n) for n=0..100.
Index to sequences with linear recurrences with constant coefficients, signature (0,0,1)
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FORMULA
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a(n) = 1 + 2*[3|n] = 1 + 2(1 + 2*cos(2*n*Pi/3])/3, where [x|y] = 1 when x divides y, 0 otherwise.
a(n) = a(n-3).
Multiplicative with a(p^e, 3) = GCD(p^e, 3). David W. Wilson Jun 12, 2005.
O.g.f.: -(3+x+x^2)/((x-1)*(x^2+x+1)) . - R. J. Mathar, Nov 24 2007
Dirichlet g.f. zeta(s)*(1+2/3^s). - R. J. Mathar, Apr 08 2011
a(n)= 2*floor(((n-1) mod 3)/2) + 1. [From Gary Detlefs, Dec, 28 2011]
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CROSSREFS
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Cf. A109004.
Cf. A026741, A130334.
Cf. A178255 (decimal expansion of (3+sqrt(17))/2). [From Klaus Brockhaus, May 24 2010]
Sequence in context: A098094 A087283 A111625 * A132951 A101685 A049653
Adjacent sequences: A109004 A109005 A109006 * A109008 A109009 A109010
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Mitch Harris
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STATUS
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approved
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