A036139 a(n) = 5^n mod 103.

1, 5, 25, 22, 7, 35, 72, 51, 49, 39, 92, 48, 34, 67, 26, 27, 32, 57, 79, 86, 18, 90, 38, 87, 23, 12, 60, 94, 58, 84, 8, 40, 97, 73, 56, 74, 61, 99, 83, 3, 15, 75, 66, 21, 2, 10, 50, 44, 14, 70, 41, 102, 98, 78, 81, 96, 68

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Crossrefs

Cf. A000351 (5^n).

Programs

GAP

List([0..60],n->PowerMod(5,n,103)); # Muniru A Asiru, Oct 17 2018

Magma

[Modexp(5, n, 103): n in [0..100]]; // Vincenzo Librandi, Sep 13 2011

Maple

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

Mathematica

PowerMod[5, Range[0, 100], 103] (* G. C. Greubel, Oct 17 2018 *)

PARI

a(n)=lift(Mod(5,103)^n) \\ Charles R Greathouse IV, Mar 22 2016

Formula

From G. C. Greubel, Oct 17 2018: (Start)

a(n) = a(n-1) - a(n-51) + a(n-52).

a(n+102) = a(n). (End)