A070425 a(n) = 7^n mod 43.

1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36, 37, 1, 7, 6, 42, 36

Offset

0,2

Comments

Sequence is periodic with length 6. Since a(21) = 42 (or -1), 43 is prime in Z[sqrt(7)]. - Alonso del Arte, Oct 12 2012

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Formula

From R. J. Mathar, Apr 20 2010: (Start)

a(n) = a(n - 1) - a(n - 3) + a(n - 4).

G..f: ( -1 - 6*x + x^2 - 37*x^3 ) / ( (x - 1)*(1 + x)*(x^2 - x + 1) ). (End)

a(n) = a(n-6). - G. C. Greubel, Mar 22 2016

Mathematica

PowerMod[7, Range[0, 74], 43] (* Alonso del Arte, Oct 12 2012 *)

Prog

(Sage) [power_mod(7, n, 43) for n in range(0, 83)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n)=lift(Mod(7, 43)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(7, n, 43): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Crossrefs

Sequence in context: A322049 A163260 A073112 * A163842 A328697 A288245

Adjacent sequences: A070422 A070423 A070424 * A070426 A070427 A070428

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved