A070410 a(n) = 7^n mod 25.

1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18, 1, 7, 24, 18

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Formula

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

a(n) = a(n-1) - a(n-2) + a(n-3).

G.f.: ( -1-6*x-18*x^2 ) / ( (x-1)*(1+x^2) ). (End)

a(n) = 25 - a(n-2), n>=2. - Vincenzo Librandi, Feb 08 2011

From G. C. Greubel, Mar 20 2016: (Start)

a(n) = a(n-4).

E.g.f.: (1/2)*(25*exp(x) - 23*cos(x) - 11*sin(x)). (End)

Mathematica

PowerMod[7, Range[0, 50], 25] (* G. C. Greubel, Mar 20 2016 *)
LinearRecurrence[{1, -1, 1}, {1, 7, 24}, 90] (* or *) PadRight[{}, 90, {1, 7, 24, 18}] (* Harvey P. Dale, Jan 07 2024 *)

Prog

(Sage) [power_mod(7, n, 25) for n in range(0, 84)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n) = lift(Mod(7, 25)^n); \\ Altug Alkan, Mar 20 2016
(Magma) [Modexp(7, n, 25): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Crossrefs

Sequence in context: A196113 A286506 A286406 * A077035 A076602 A287132

Adjacent sequences: A070407 A070408 A070409 * A070411 A070412 A070413

Keyword

nonn

Author

N. J. A. Sloane, May 12 2002

Status

approved