A036127 a(n) = 5^n mod 47.

1, 5, 25, 31, 14, 23, 21, 11, 8, 40, 12, 13, 18, 43, 27, 41, 17, 38, 2, 10, 3, 15, 28, 46, 42, 22, 16, 33, 24, 26, 36, 39, 7, 35, 34, 29, 4, 20, 6, 30, 9, 45, 37, 44, 32, 19, 1, 5, 25, 31, 14, 23, 21, 11, 8, 40, 12, 13, 18, 43

Offset

0,2

References

I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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,-1,1).

Formula

a(n) = (n-46). - Vincenzo Librandi, Feb 07 2011

a(n) = a(n-1) - a(n-23) + a(n-24). - R. J. Mathar, Jun 04 2016

a(n) = 47 - a(n+23) for all n in Z. - Michael Somos, Oct 17 2018

Maple

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

Mathematica

Mod[5^Range[0, 100], 47]  (* Harvey P. Dale, Mar 09 2011 *)

Prog

(PARI) a(n)=lift(Mod(5, 47)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(5, n, 47): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..60], n->PowerMod(5, n, 47)); # Muniru A Asiru, Oct 18 2018

Crossrefs

Cf. A000351 (5^n).

Sequence in context: A000221 A018612 A395266 * A291755 A018639 A029475

Adjacent sequences: A036124 A036125 A036126 * A036128 A036129 A036130

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved