A036129 a(n) = 2^n mod 59.

1, 2, 4, 8, 16, 32, 5, 10, 20, 40, 21, 42, 25, 50, 41, 23, 46, 33, 7, 14, 28, 56, 53, 47, 35, 11, 22, 44, 29, 58, 57, 55, 51, 43, 27, 54, 49, 39, 19, 38, 17, 34, 9, 18, 36, 13, 26, 52, 45, 31, 3, 6, 12, 24, 48, 37, 15

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

Programs

GAP

List([0..70],n->PowerMod(2,n,59)); # Muniru A Asiru, Jan 30 2019

Magma

[Modexp(2, n, 59): n in [0..100]]; // G. C. Greubel, Oct 17 2018

Maple

i := pi(59) ; [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];

Mathematica

PowerMod[2, Range[0, 100], 59] (* G. C. Greubel, Oct 17 2018 *)

PARI

a(n)=lift(Mod(2,59)^n) \\ Charles R Greathouse IV, Mar 22 2016

Formula

a(n) = a(n+58). - R. J. Mathar, Jun 04 2016

a(n) = a(n-1) - a(n-29) + a(n-30). - G. C. Greubel, Oct 17 2018