login
A036121
5^n mod 23.
3
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved