A036137 a(n) = 5^n mod 97.

1, 5, 25, 28, 43, 21, 8, 40, 6, 30, 53, 71, 64, 29, 48, 46, 36, 83, 27, 38, 93, 77, 94, 82, 22, 13, 65, 34, 73, 74, 79, 7, 35, 78, 2, 10, 50, 56, 86, 42, 16, 80, 12, 60, 9, 45, 31, 58, 96, 92, 72, 69, 54, 76, 89, 57, 91, 67

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,-1,1).

Formula

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

a(n) = a(n-1) - a(n-48) + a(n-49).

a(n+96) = a(n). (End)

Example

As 5^5 = 3125 = k * 97 + 21 for some k and 0 <= 21 < 97, a(5) = 21. - David A. Corneth, Oct 17 2018

Maple

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

Mathematica

PowerMod[5, Range[0, 100], 97] (* G. C. Greubel, Oct 17 2018 *)

Prog

(PARI) a(n)=lift(Mod(5, 97)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Python) for n in range(0, 100): print(int(pow(5, n, 97)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(5, n, 97)); # Muniru A Asiru, Oct 17 2018
(Magma) [Modexp(5, n, 97): n in [0..100]]; // G. C. Greubel, Oct 18 2018

Crossrefs

Cf. A000351 (5^n).

Sequence in context: A136912 A137111 A137110 * A070380 A068574 A000350

Adjacent sequences: A036134 A036135 A036136 * A036138 A036139 A036140

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved