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

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn

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).

Programs

Magma

[Modexp(5, n, 37): n in [0..100]]; // Vincenzo Librandi, Jun 29 2016

Mathematica

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

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

Sage

[power_mod(5,n,37) for n in range(0,76)] # Zerinvary Lajos, Nov 26 2009

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