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

0,2

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).

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)

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 *)

Prog

(Magma) [Modexp(5, n, 103): n in [0..100]]; // Vincenzo Librandi, Sep 13 2011
(PARI) a(n)=lift(Mod(5, 103)^n) \\ Charles R Greathouse IV, Mar 22 2016
(GAP) List([0..60], n->PowerMod(5, n, 103)); # Muniru A Asiru, Oct 17 2018

Crossrefs

Cf. A000351 (5^n).

Sequence in context: A070383 A070061 A070376 * A070382 A271379 A192493

Adjacent sequences: A036136 A036137 A036138 * A036140 A036141 A036142

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved