A036135 a(n) = 2^n mod 83.

1, 2, 4, 8, 16, 32, 64, 45, 7, 14, 28, 56, 29, 58, 33, 66, 49, 15, 30, 60, 37, 74, 65, 47, 11, 22, 44, 5, 10, 20, 40, 80, 77, 71, 59, 35, 70, 57, 31, 62, 41, 82, 81, 79, 75, 67, 51, 19, 38, 76, 69, 55, 27, 54, 25, 50, 17

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,-1,1).

Formula

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

a(n) = a(n-1) - a(n-41) + a(n-42).

a(n+82) = a(n). (End)

Maple

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

Mathematica

PowerMod[2, Range[0, 100], 83] (* G. C. Greubel, Oct 17 2018 *)

Prog

(PARI) a(n)=lift(Mod(2, 83)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Python) for n in range(0, 100): print(int(pow(2, n, 83)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(2, n, 83)); # Muniru A Asiru, Oct 17 2018
(Magma) [Modexp(2, n, 83): n in [0..100]]; // G. C. Greubel, Oct 18 2018

Crossrefs

CF. A000079 (2^n).

Sequence in context: A036140 A036138 A000855 * A036131 A115424 A225878

Adjacent sequences: A036132 A036133 A036134 * A036136 A036137 A036138

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved