A070415 a(n) = 7^n mod 31.

1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4, 28, 10, 8, 25, 20, 16, 19, 9, 1, 7, 18, 2, 14, 5, 4

Offset

0,2

Comments

Sequence is periodic with period length of 15. That a(15) = 1 means that 31 is not prime in Z[sqrt(7)], being factorable as (-1)*(9 - 4*sqrt(7))(9 + 4*sqrt(7)). - Alonso del Arte, Oct 11 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, 0, 0, 0, 0, 0, 0, 1).

Formula

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

a(n) = a(n - 15).

G.f.: ( -1 -7*x -18*x^2 -2*x^3 -14*x^4 -5*x^5 -4*x^6 -28*x^7 -10*x^8 -8*x^9 -25*x^10 -20*x^11 -16*x^12 -19*x^13 -9*x^14 ) / ( (x-1)*(1 +x^4 + x^3 +x^2 +x)*(1 +x +x^2)*(1 -x +x^3 -x^4 +x^5 -x^7 +x^8) ). (End)

Mathematica

PowerMod[7, Range[0, 90], 31] (* Harvey P. Dale, Jul 23 2011 *)

Prog

(Sage) [power_mod(7, n, 31) for n in range(0, 82)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n) = lift(Mod(7, 31)^n); \\ Altug Alkan, Mar 20 2016
(Magma) [Modexp(7, n, 31): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Crossrefs

Sequence in context: A138491 A022511 A113613 * A034083 A185455 A103570

Adjacent sequences: A070412 A070413 A070414 * A070416 A070417 A070418

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved