A036126 a(n) = 3^n mod 43.

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

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,-1,1).

Formula

a(n) = a(n-1) - a(n-21) + a(n-22). - R. J. Mathar, Feb 08 2011

a(n) = a(n+42). - R. J. Mathar, Jun 04 2016

a(n) = 43 - a(n+21) for all n in Z. - Michael Somos, Oct 17 2018

Maple

i := pi(43) ; [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];

Mathematica

PowerMod[3, Range[0, 100], 43] (* G. C. Greubel, Oct 16 2018 *)
PadRight[{}, 120, {1, 3, 9, 27, 38, 28, 41, 37, 25, 32, 10, 30, 4, 12, 36, 22, 23, 26, 35, 19, 14, 42, 40, 34, 16, 5, 15, 2, 6, 18, 11, 33, 13, 39, 31, 7, 21, 20, 17, 8, 24, 29}] (* Harvey P. Dale, Mar 30 2019 *)

Prog

(PARI) a(n)=lift(Mod(3, 43)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 43): n in [0..100]]; // G. C. Greubel, Oct 18 2018
(GAP) List([0..60], n->PowerMod(3, n, 43)); # Muniru A Asiru, Oct 18 2018

Crossrefs

Cf. A000244 (3^n).

Sequence in context: A027889 A360423 A018766 * A045580 A070361 A056024

Adjacent sequences: A036123 A036124 A036125 * A036127 A036128 A036129

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved