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A070420 a(n) = 7^n mod 37. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 29 05:59 EDT 2021. Contains 346340 sequences. (Running on oeis4.)