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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 ) / ( (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 xrange(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

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.