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A010687
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Repeat (1,6): Period 2.
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6
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1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6
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OFFSET
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0,2
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COMMENTS
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Continued fraction for (3+sqrt(15))/6. - Philippe Deléham, Sep 25 2006
This sequence can be generated by an infinite number of formulas all having the form a^(b*n) mod c subject to the following conditions. The number a can be congruent to either 3,5 or 6 mod 7. If a is congruent to 3 or 5 mod 7 then b can be any number of the form 3*k+6. If a is congruent to 6 mod 7 then b can be any number of the form 2k+1. Finally, if a is congruent to either 6, 26, or 31 mod 35 then c can be 7 or 35; otherwise, we use c = 7. For example: a(n) = 33^(15*n) mod 7, a(n) = 31^(9*n) mod 7, and a(n) = 31^(9*n) mod 35. - Gary Detlefs, May 19 2014
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LINKS
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Table of n, a(n) for n=0..85.
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FORMULA
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G.f.: (1+6*x)/(1-x^2). - Philippe Deléham, Sep 25 2006
a(n) = 5/2*(-1)^n+7/2. a(n) = 6*(n mod 2)+((n+1) mod 2). - Paolo P. Lava, Oct 20 2006
a(n) = 6^n mod 7. - Zerinvary Lajos, Nov 26 2009
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MAPLE
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A010687:=n->(6^n mod 7); seq(A010687(n), n=0..100); # Wesley Ivan Hurt, May 19 2014
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MATHEMATICA
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Table[Mod[6^n, 7], {n, 0, 100}] (* Wesley Ivan Hurt, May 19 2014 *)
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PROG
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(Sage) [power_mod(6, n, 7)for n in range(0, 100)] # Zerinvary Lajos, Nov 26 2009
(PARI) a(n)=n%2*5+1 \\ Charles R Greathouse IV, Jul 13 2016
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CROSSREFS
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Sequence in context: A193239 A023406 A138116 * A176355 A109918 A263494
Adjacent sequences: A010684 A010685 A010686 * A010688 A010689 A010690
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 11 1996
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STATUS
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approved
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