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

0,2

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, -1, 1).

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

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 *)

Prog

(Sage) [power_mod(5, n, 23)for n in range(0, 63)] # - Zerinvary Lajos, Nov 26 2009
(Magma) [Modexp(5, n, 23): n in [0..100]]; // Vincenzo Librandi, Feb 07 2011
(PARI) a(n)=lift(Mod(5, 23)^n) \\ Charles R Greathouse IV, Mar 22 2016

Crossrefs

Sequence in context: A040024 A196385 A178714 * A162396 A194046 A249368

Adjacent sequences: A036118 A036119 A036120 * A036122 A036123 A036124

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved