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

0,2

Comments

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

Links

Table of n, a(n) for n=0..79.

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

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 *)

Prog

(Sage) [power_mod(7, n, 23) for n in range(0, 80)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n) = lift(Mod(7, 23)^n); \\ Michel Marcus, Feb 23 2015
(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

Crossrefs

Sequence in context: A160797 A050013 A161417 * A166481 A050012 A271573

Adjacent sequences: A070406 A070407 A070408 * A070410 A070411 A070412

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved