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A100402 Digital root of 4^n. 9
1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals A141725 mod 9. - Paul Curtz, Sep 15 2008

Sequence is the digital root of A016777. - Odimar Fabeny, Sep 13 2010

Digital root of the powers of any number congruent to 4 mod 9. - Alonso del Arte, Jan 26 2014

Period 3: repeat [1, 4, 7]. - Wesley Ivan Hurt, Aug 26 2014

REFERENCES

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

LINKS

Table of n, a(n) for n=0..104.

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

FORMULA

a(n) = 4^n mod 9. - Zerinvary Lajos, Nov 25 2009

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-3) for n>2.

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

a(n) = A010888(A000302(n)). - Michel Marcus, Aug 25 2014

a(n) = 3*A010872(n) + 1. - Robert Israel, Aug 25 2014

a(n) = 4 - 3*cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3). - Wesley Ivan Hurt, Jun 30 2016

EXAMPLE

4^2 = 16, digitalroot(16) = 7, the third entry.

MAPLE

A100402:=n->4^n mod 9: seq(A100402(n), n=0..100); # Wesley Ivan Hurt, Aug 26 2014

MATHEMATICA

Table[Mod[4^n, 9], {n, 0, 99}] (* Alonso del Arte, Jan 26 2014 *)

PROG

(Sage) [power_mod(4, n, 9)for n in range(0, 105)] # Zerinvary Lajos, Nov 25 2009

(MAGMA) [4^n mod 9 : n in [0..100]]; // Wesley Ivan Hurt, Aug 26 2014

(PARI) a(n)=[1, 4, 7][1+n%3]; \\ Joerg Arndt, Aug 26 2014

CROSSREFS

Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 5, A070366; c = 7, A070403; c = 8, A010689.

Cf. A000302, A010872, A010888, A141725, A016777.

Sequence in context: A123734 A011519 A131594 * A135004 A086234 A016490

Adjacent sequences:  A100399 A100400 A100401 * A100403 A100404 A100405

KEYWORD

easy,nonn,base

AUTHOR

Cino Hilliard, Dec 31 2004

STATUS

approved

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Last modified November 30 20:55 EST 2020. Contains 338812 sequences. (Running on oeis4.)