A036123 a(n) = 3^n mod 31.

1, 3, 9, 27, 19, 26, 16, 17, 20, 29, 25, 13, 8, 24, 10, 30, 28, 22, 4, 12, 5, 15, 14, 11, 2, 6, 18, 23, 7, 21, 1, 3, 9, 27, 19, 26, 16, 17, 20, 29, 25, 13, 8, 24, 10, 30, 28, 22, 4, 12, 5, 15, 14, 11, 2, 6, 18, 23, 7, 21, 1, 3

Offset

0,2

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 (1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

Formula

a(n) = a(n+30). - R. J. Mathar, Jun 04 2016

a(n) = a(n-1) - a(n-15) + a(n-16). - G. C. Greubel, Oct 16 2018

a(n) = 31 - a(n+15) for all n in Z. - Michael Somos, Oct 17 2018

Maple

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

Mathematica

PowerMod[3, Range[0, 100], 31] (* G. C. Greubel, Oct 16 2018 *)

Prog

(PARI) a(n)=lift(Mod(3, 31)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 31): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..65], n->PowerMod(3, n, 31)); # Muniru A Asiru, Oct 18 2018

Crossrefs

Cf. A000244 (3^n).

Sequence in context: A070358 A321542 A321540 * A168427 A070344 A070357

Adjacent sequences: A036120 A036121 A036122 * A036124 A036125 A036126

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved