

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(n1)  a(n11) + a(n12).
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 ) / ( (x1)*(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(n1)Self(n11)+Self(n12): 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,changed


AUTHOR

N. J. A. Sloane, May 12 2002


STATUS

approved



