login
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
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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 12 2002
STATUS
approved