A036125 a(n) = 6^n mod 41.

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

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,-1,1).

Formula

a(n) = a(n+40). - R. J. Mathar, Jun 04 2016

a(n) = a(n-1) - a(n-20) + a(n-21). - G. C. Greubel, Oct 16 2018

a(n) = 41 - a(n+20) for all n in Z. - Michael Somos, Oct 17 2018

Maple

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

Mathematica

PowerMod[6, Range[0, 60], 41] (* Harvey P. Dale, Jul 08 2017 *)

Prog

(PARI) a(n)=lift(Mod(6, 41)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(6, n, 41): n in [0..100]]; // G. C. Greubel, Oct 16 2018
(GAP) List([0..65], n->PowerMod(6, n, 41)); # Muniru A Asiru, Oct 18 2018

Crossrefs

Cf. A000400 (6^n).

Sequence in context: A304255 A050112 A250202 * A001311 A360442 A137868

Adjacent sequences: A036122 A036123 A036124 * A036126 A036127 A036128

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved