A070384 a(n) = 5^n mod 37.

1, 5, 25, 14, 33, 17, 11, 18, 16, 6, 30, 2, 10, 13, 28, 29, 34, 22, 36, 32, 12, 23, 4, 20, 26, 19, 21, 31, 7, 35, 27, 24, 9, 8, 3, 15, 1, 5, 25, 14, 33, 17, 11, 18, 16, 6, 30, 2, 10, 13, 28, 29, 34, 22, 36, 32, 12, 23, 4, 20, 26, 19, 21, 31, 7, 35, 27, 24, 9, 8, 3, 15, 1, 5, 25, 14

Offset

0,2

Comments

Period: (1, 5, 25, 14, 33, 17, 11, 18, 16, 6, 30, 2, 10, 13, 28, 29, 34, 22, 36, 32, 12, 23, 4, 20, 26, 19, 21, 31, 7, 35, 27, 24, 9, 8, 3, 15) of length 36. - Zak Seidov, Feb 08 2011

Links

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

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Formula

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

a(n) = a(n-1) - a(n-18) + a(n-19).

G.f.: ( -1-4*x-20*x^2+11*x^3-19*x^4+16*x^5+6*x^6-7*x^7 +2*x^8+10*x^9 -24*x^10+28*x^11-8*x^12-3*x^13-15*x^14-x^15-5*x^16+12*x^17-15*x^18 ) / ( (x-1)*(x^2+1)*(x^4-x^2+1)*(x^12-x^6+1) ). (End)

a(n) = 37 - a(n-18). - Zak Seidov, Feb 08 2011

a(n) = a(n-36). - G. C. Greubel, Mar 16 2016

Mathematica

a[n_]:=PowerMod[5, n, 37]; Table[a[n], {n, 72}] (* Zak Seidov, Feb 08 2011 *)

Prog

(SageMath) [power_mod(5, n, 37) for n in range(0, 76)] # Zerinvary Lajos, Nov 26 2009
(PARI) a(n)=lift(Mod(5, 37)^n) \\ M. F. Hasler, Feb 08 2011
(PARI) a(n)=5^(n%36)%37  \\ M. F. Hasler, Feb 08 2011
(Magma) [Modexp(5, n, 37): n in [0..100]]; // Vincenzo Librandi, Jun 29 2016

Crossrefs

Sequence in context: A070385 A328756 A070378 * A337392 A070377 A070383

Adjacent sequences: A070381 A070382 A070383 * A070385 A070386 A070387

Keyword

nonn

Author

N. J. A. Sloane, May 12 2002

Status

approved