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A070409 a(n) = 7^n mod 23. 1
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 (list; graph; refs; listen; history; text; internal format)
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 xrange(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

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Last modified November 21 12:43 EST 2017. Contains 295001 sequences.