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
(Sage) [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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved