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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000244 (3^n).

Programs

GAP

List([0..65],n->PowerMod(3,n,31)); # Muniru A Asiru, Oct 18 2018

Magma

[Modexp(3, n, 31): n in [0..100]]; // G. C. Greubel, Oct 18 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 *)

PARI

a(n)=lift(Mod(3,31)^n) \\ Charles R Greathouse IV, Mar 22 2016

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