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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A008831.

Programs

GAP

List([0..95],n->PowerMod(2,n,13)); # Muniru A Asiru, Jan 31 2019

Magma

[2^n mod 13: n in [0..100]]; // G. C. Greubel, Oct 16 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 *)

PARI

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

Sage

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

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