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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A000351 (5^n).

Programs

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

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 *)

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

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)