A070403 a(n) = 7^n mod 9.

1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4, 1, 7, 4

Offset

0,2

Comments

Also the digital root of 7^n. If we convert this to a repeating decimal 0.174174..., we get the rational number 58/333. - Cino Hilliard, Dec 31 2004

A141722 (1, 25, 121, 505, 2041, 8185) mod 9. Note A141722 = 10*A000975(2n) + A000975(2n+1). - Paul Curtz, Sep 15 2008

Digital root of the powers of any number congruent to 7 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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

From R. J. Mathar, Feb 23 2009: (Start)

G.f.: (1+7*x+4*x^2)/((1-x)*(1+x+x^2)).

a(n+1) - a(n) = 3*A099837(n+3).

a(n) = 4 - 3*A049347(n). (End)

a(n) = a(n-3) for n>3. - G. C. Greubel, Mar 19 2016

a(n) = 4-2*sqrt(3)*sin((2*n+2)*Pi/3). - Wesley Ivan Hurt, Jun 09 2016

Maple

A070403:=n->4-2*sqrt(3)*sin(2*(n+1)*Pi/3): seq(A070403(n), n=0..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Table[PowerMod[7, n, 9], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)

Prog

(Sage) [power_mod(7, n, 9)for n in range(0, 105)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=7^n%9 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [Modexp(7, n, 9): n in [0..110]]; // Bruno Berselli, Mar 22 2016

Crossrefs

Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 4, A100402; c = 5, A070366; c = 8, A010689.

Cf. A049347, A099837.

Sequence in context: A199157 A328416 A010508 * A144468 A237042 A258225

Adjacent sequences: A070400 A070401 A070402 * A070404 A070405 A070406

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved