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A036118

a(n) = 2^n mod 13.

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

0,2

COMMENTS

The sequence is 12-periodic.

REFERENCES

I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,-1,1).

FORMULA

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

MAPLE

[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];

MATHEMATICA

PowerMod[2, Range[0, 70], 13] (* Wesley Ivan Hurt, Nov 20 2014 *)

PROG

(SageMath) [power_mod(2, n, 13) for n in range(0, 72)] # Zerinvary Lajos, Nov 03 2009

(PARI) a(n)=2^n%13 \\ Charles R Greathouse IV, Oct 07 2015

(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