A036141 a(n) = 6^n mod 109.

1, 6, 36, 107, 97, 37, 4, 24, 35, 101, 61, 39, 16, 96, 31, 77, 26, 47, 64, 57, 15, 90, 104, 79, 38, 10, 60, 33, 89, 98, 43, 40, 22, 23, 29, 65, 63, 51, 88, 92, 7, 42, 34, 95, 25, 41, 28, 59, 27, 53, 100, 55, 3, 18, 108

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Formula

From G. C. Greubel, Oct 18 2018: (Start)

a(n + 108) = a(n).

a(n) = a(n-1) - a(n-54) + a(n-55). (End)

Maple

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

Mathematica

PowerMod[6, Range[0, 60], 109] (* Harvey P. Dale, Apr 27 2018 *)

Prog

(PARI) a(n)=lift(Mod(6, 109)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(6, n, 109): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..55], n->PowerMod(6, n, 109)); # Muniru A Asiru, Oct 18 2018

Crossrefs

Cf. A000400 (6^n).

Sequence in context: A207495 A207249 A060521 * A270205 A207443 A207437

Adjacent sequences: A036138 A036139 A036140 * A036142 A036143 A036144

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved