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A036118
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a(n) = 2^n mod 13.
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7
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1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7
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OFFSET
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0,2
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COMMENTS
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The sequence is 12-periodic.
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REFERENCES
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I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
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LINKS
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FORMULA
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a(n) = 13/2 + (-5/3 - (2/3)*sqrt(3))*cos(Pi*n/6) + (-1/3 - sqrt(3))*sin(Pi*n/6) - (13/6)*cos(Pi*n/2) - (13/6)*sin(Pi*n/2) + (-5/3 + (2/3)*sqrt(3))*cos(5*Pi*n/6) + (sqrt(3) - 1/3)*sin(5*Pi*n/6). - Richard Choulet, Dec 12 2008
a(n) = a(n-1) - a(n-6) + a(n-7). - R. J. Mathar, Apr 13 2010
G.f.: (1 + x + 2*x^2 + 4*x^3 - 5*x^4 + 3*x^5 + 7*x^6)/ ((1-x) * (x^2+1) * (x^4 - x^2 + 1)). - R. J. Mathar, Apr 13 2010
a(n) = 13 - a(n+6) = a(n+12) for all n in Z. - Michael Somos, Oct 17 2018
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MAPLE
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[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
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MATHEMATICA
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PROG
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(Sage) [power_mod(2, n, 13) for n in range(0, 72)] # Zerinvary Lajos, Nov 03 2009
(Magma) [2^n mod 13: n in [0..100]]; // G. C. Greubel, Oct 16 2018
(GAP) List([0..95], n->PowerMod(2, n, 13)); # Muniru A Asiru, Jan 31 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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