A070409 a(n) = 7^n mod 23.

1, 7, 3, 21, 9, 17, 4, 5, 12, 15, 13, 22, 16, 20, 2, 14, 6, 19, 18, 11, 8, 10, 1, 7, 3, 21, 9, 17, 4, 5, 12, 15, 13, 22, 16, 20, 2, 14, 6, 19, 18, 11, 8, 10, 1, 7, 3, 21, 9, 17, 4, 5, 12, 15, 13, 22, 16, 20, 2, 14, 6, 19, 18, 11, 8, 10, 1, 7, 3, 21, 9, 17, 4, 5, 12, 15, 13, 22, 16, 20

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Periodic with period 22. - Joerg Arndt, Feb 24 2015

Links

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

Programs

Magma

I:=[1,7,3,21,9,17,4,5,12,15,13,22]; [n le 12 select I[n] else Self(n-1)-Self(n-11)+Self(n-12): n in [1..70]]; // Vincenzo Librandi, Feb 26 2015

Magma

[Modexp(7, n, 23): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Mathematica

Table[PowerMod[7, n, 23], {n, 0, 79}] (* Alonso del Arte, Feb 23 2015 *)
CoefficientList[Series[(- 1 - 6 x + 4 x^2 - 18 x^3 + 12 x^4 - 8 x^5 + 13 x^6 - x^7 - 7 x^8 - 3 x^9 + 2 x^10 - 10 x^11) / ((x - 1) (1 + x) (x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)), {x, 0, 80}], x] (* Vincenzo Librandi, Feb 26 2015 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1},{1, 7, 3, 21, 9, 17, 4, 5, 12, 15, 13, 22},80] (* Ray Chandler, Aug 27 2015 *)

PARI

a(n) = lift(Mod(7, 23)^n); \\ Michel Marcus, Feb 23 2015

Sage

[power_mod(7,n,23) for n in range(0,80)] # Zerinvary Lajos, Nov 27 2009

Formula

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

a(n) = a(n-1) - a(n-11) + a(n-12).

G.f.: ( -1 - 6*x + 4*x^2 - 18*x^3 + 12*x^4 - 8*x^5 + 13*x^6 - x^7 - 7*x^8 - 3*x^9 + 2*x^10 - 10*x^11 ) / ( (x-1)*(1+x)*(x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1) ). (End)

a(n) = A000420(n) mod 23. - Michel Marcus, Feb 24 2015