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

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

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).

Programs

Magma

[Modexp(7, n, 43): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Mathematica

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

PARI

a(n)=lift(Mod(7,43)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(7,n,43) for n in range(0,83)] # Zerinvary Lajos, Nov 27 2009

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