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A070403 a(n) = 7^n mod 9. 8
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 (list; graph; refs; listen; history; text; internal format)
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

a(n) = (1/3)*(7*(n mod 3) + 7*((n+1) mod 3) - 2*((n+2) mod 3)). - Paolo P. Lava, Oct 21 2008

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) = 4 + 4/3 * (-1/2 - (1/2*i) * sqrt(3))^(-2) * (-1/2 - (1/2*i) * sqrt(3))^n + 4/3 * (-1/2 + (1/2*i) * sqrt(3))^(-2) * (-1/2 + (1/2*i) * sqrt(3))^n + 1/3 * (-1/2 - (1/2*i) * sqrt(3))^n + 1/3 * (-1/2  + (1/2*i) * sqrt(3))^n + 7/3 * (-1/2 - (1/2*i) * sqrt(3))^(-1) * (-1/2 - (1/2*i) * sqrt(3))^n + 7/3 * (-1/2 + (1/2*i) * sqrt(3))^(-1) * (-1/2 + (1/2*i)*sqrt(3))^n, with n >= 0 and i = sqrt(-1). - Paolo P. Lava, Feb 25 2010

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 xrange(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: A010138 A199157 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

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Last modified July 23 22:47 EDT 2019. Contains 325278 sequences. (Running on oeis4.)