A036121 5^n mod 23.

1, 5, 2, 10, 4, 20, 8, 17, 16, 11, 9, 22, 18, 21, 13, 19, 3, 15, 6, 7, 12, 14, 1, 5, 2, 10, 4, 20, 8, 17, 16, 11, 9, 22, 18, 21, 13, 19, 3, 15, 6, 7, 12, 14, 1, 5, 2, 10, 4, 20, 8, 17, 16, 11, 9, 22, 18, 21, 13, 19, 3, 15, 6, 7, 12, 14, 1, 5, 2, 10, 4, 20, 8

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, -1, 1).

Programs

Magma

[Modexp(5, n, 23): n in [0..100]]; // Vincenzo Librandi, Feb 07 2011

Maple

with(numtheory): i=9: [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];

Mathematica

Mod[5^Range[0, 50], 23] (* Wesley Ivan Hurt, Jul 06 2014 *)
PowerMod[5,Range[0,80],23] (* or *) PadRight[{},80,{1,5,2,10,4,20,8,17,16,11,9,22,18,21,13,19,3,15,6,7,12,14}] (* Harvey P. Dale, Jul 10 2018 *)

PARI

a(n)=lift(Mod(5,23)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(5,n,23)for n in range(0,63)] # - Zerinvary Lajos, Nov 26 2009

Formula

a(n) = +a(n-1) -a(n-11) +a(n-12). G.f.: ( -1-4*x+3*x^2-8*x^3+6*x^4-16*x^5+12*x^6-9*x^7+x^8+5*x^9+2*x^10-14*x^11 ) / ( (x-1)*(1+x)*(x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) ). - R. J. Mathar, Apr 20 2010

a(n) = a(n+22). - R. J. Mathar, Jun 04 2016