A036136 a(n) = 3^n mod 89.

1, 3, 9, 27, 81, 65, 17, 51, 64, 14, 42, 37, 22, 66, 20, 60, 2, 6, 18, 54, 73, 41, 34, 13, 39, 28, 84, 74, 44, 43, 40, 31, 4, 12, 36, 19, 57, 82, 68, 26, 78, 56, 79, 59, 88, 86, 80, 62, 8, 24, 72, 38, 25, 75, 47, 52, 67, 23

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,-1,1).

Formula

From G. C. Greubel, Oct 17 2018: (Start)

a(n) = a(n-1) - a(n-44) + a(n-45).

a(n+88) = a(n). (End)

Maple

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

Mathematica

PowerMod[3, Range[0, 100], 89] (* G. C. Greubel, Oct 17 2018 *)

Prog

(PARI) a(n)=lift(Mod(3, 89)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 89): n in [0..100]]; // G. C. Greubel, Oct 17 2018
(Python) for n in range(0, 100): print(int(pow(3, n, 89)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(3, n, 89)); # Muniru A Asiru, Oct 17 2018

Crossrefs

Cf. A000244 (3^n).

Sequence in context: A329023 A001218 A036158 * A271350 A057262 A057232

Adjacent sequences: A036133 A036134 A036135 * A036137 A036138 A036139

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved