A070420 a(n) = 7^n mod 37.

1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9, 26, 34, 16, 1, 7, 12, 10, 33, 9

Offset

0,2

Comments

Sequence is periodic with length 9. Since a(18) = 1, 37 is composite in Z[sqrt(7)]: it can be factored as (10 - 3*sqrt(7))(10 + 3*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 (0,0,0,0,0,0,0,0,1).

Formula

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

a(n) = a(n - 9).

G.f.: ( -1 - 7*x - 12*x^2 - 10*x^3 - 33*x^4 - 9*x^5 - 26*x^6 - 34*x^7 - 16*x^8 ) / ( (x - 1)*(1 + x + x^2)*(x^6 + x^3 + 1) ). (End)

Example

a(2) = 12 because 7^2 = 49 and 49 - 37 = 12.

Mathematica

PowerMod[7, Range[0, 74], 37] (* Alonso del Arte, Oct 12 2012 *)

Prog

(Sage) [power_mod(7, n, 37) for n in range(0, 78)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n) = lift(Mod(7, 37)^n); \\ Michel Marcus, Mar 21 2016
(Magma) [Modexp(7, n, 37): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Crossrefs

Sequence in context: A038598 A180570 A074474 * A223423 A274334 A328414

Adjacent sequences: A070417 A070418 A070419 * A070421 A070422 A070423

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved