

A070415


a(n) = 7^n mod 31.


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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


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 ) / ( (x1)*(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



