A070366 a(n) = 5^n mod 9.

1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7

Offset

0,2

Comments

Period 6: repeat [1, 5, 7, 8, 4, 2].

Also the digital root of 5^n. - Cino Hilliard, Dec 31 2004

Digital root of the powers of any number congruent to 5 mod 9. - Alonso del Arte, Jan 26 2014

References

Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.

G.f.: ( 1+4*x+2*x^2+2*x^3 ) / ( (1-x)*(1+x)*(x^2-x+1) ). (End)

a(n) = 1/2^n (mod 9), n >= 0. - Wolfdieter Lang, Feb 18 2014

a(n) = A010878(A000351(n)). - Michel Marcus, Feb 20 2014

From G. C. Greubel, Mar 05 2016: (Start)

a(n) = a(n-6) for n>5.

E.g.f.: (1/2)*(9*exp(x) - exp(-x) + 2*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) - 6*exp(x/2)*cos(sqrt(3)*x/2)). (End)

a(n) = (9 - cos(n*Pi) - 6*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/2. - Wesley Ivan Hurt, Jun 28 2016

a(n) = 2^((-n) mod 6) mod 9. - Joe Slater, Mar 23 2017

Maple

A070366:=n->power(5, n) mod 9: seq(A070366(n), n=0..100); # Wesley Ivan Hurt, Jun 28 2016

Mathematica

PowerMod[5, Range[0, 120], 9] (* Harvey P. Dale, Mar 27 2011 *)
Table[Mod[5^n, 9], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)

Prog

(PARI) a(n)=lift(Mod(5, 9)^n); \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [Modexp(5, n, 9): n in [0..100]]; // Wesley Ivan Hurt, Jun 28 2016

Crossrefs

Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 4, A100402; c = 7, A070403; c = 8, A010689.

Cf. A000351, A010878.

Sequence in context: A244355 A245278 A155855 * A339986 A141606 A354051

Adjacent sequences: A070363 A070364 A070365 * A070367 A070368 A070369

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved