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

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

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).

Crossrefs

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

Cf. A000975, A010888, A049347, A099837, A141722.

Programs

Magma

[Modexp(7, n, 9): n in [0..110]]; // Bruno Berselli, Mar 22 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 *)

PARI

a(n)=7^n%9 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[power_mod(7,n,9)for n in range(0,105)] # Zerinvary Lajos, Nov 03 2009

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

a(n) = A010888(7*a(n-1)). - Stefano Spezia, Mar 20 2025