A153130 Period 6: repeat [1, 2, 4, 8, 7, 5].

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

Offset

0,2

Comments

Digital root of 2^n.

A regular version of Pitoun's sequence: a(n) = A029898(n+1).

Also obtained from permutations of A141425, A020806, A070366, A153110, A153990, A154127, A154687, or A154815.

This sequence and its (again period 6) repeated differences produce the table:

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

1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, ...

1, 2, -5, -1, -2, 5, 1, 2, -5, -1, -2, ...

1, -7, 4, -1, 7, -4, 1, -7, 4, -1, 7, ...

-8, 11, -5, 8,-11, 5, -8, 11, -5, 8,-11, ...

19,-16, 13,-19, 16,-13, 19,-16, 13,-19, 16, ...

-35, 29,-32, 35,-29, 32,-35, 29,-32, 35,-29, ...

64,-61, 67,-64, 61,-67, 64,-61, 67,-64, 61, ...

If each entry of this table is read modulo 9 we obtain the very regular table:

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

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

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

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

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

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

Also the decimal expansion of the constant 125/1001. - R. J. Mathar, Jan 23 2009

Digital root of the powers of any number congruent to 2 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

Table of n, a(n) for n=0..107.

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

Formula

a(n) + a(n+3) = 9 = A010734(n).

G.f.: (1+x+2x^2+5x^3)/((1-x)(1+x)(1-x+x^2)). - R. J. Mathar, Jan 23 2009

a(n) = A082365(n) mod 9. - Paul Curtz, Mar 31 2009

a(n) = -1/2*cos(Pi*n) - 3*cos(1/3*Pi*n) - 3^(1/2)*sin(1/3*Pi*n) + 9/2. - Leonid Bedratyuk, May 13 2012

a(n) = A010888(A004000(n+1)). - Ivan N. Ianakiev, Nov 27 2014

From Wesley Ivan Hurt, Apr 20 2015: (Start)

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

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

a(n) = (2+3*(n-1 mod 3))*(n mod 2) + (1+3*(-n mod 3))*(n-1 mod 2). (End)

a(n) = 2^n mod 9. - Nikita Sadkov, Oct 06 2018

Maple

seq(op([1, 2, 4, 8, 7, 5]), n=0..40); # Wesley Ivan Hurt, Jul 05 2016

Mathematica

Flatten[Table[{1, 2, 4, 8, 7, 5}, {20}]] (* Paul Curtz, Dec 19 2008 *)
Table[Mod[2^n, 9], {n, 0, 99}] (* Alonso del Arte, Jan 26 2014 *)

Prog

(PARI) a(n)=lift(Mod(2, 9)^n) \\ Charles R Greathouse IV, Apr 21 2015
(Magma) &cat [[1, 2, 4, 8, 7, 5]^^30]; // Wesley Ivan Hurt, Jul 05 2016

Crossrefs

Cf. A030132, A145389, A189510.

Cf. digital roots of powers of c mod 9: c = 4, A100402; c = 5, A070366; c = 7, A070403; c = 8, A010689.

Sequence in context: A071571 A201568 A029898 * A225746 A021406 A065075

Adjacent sequences: A153127 A153128 A153129 * A153131 A153132 A153133

Keyword

nonn,easy

Author

Paul Curtz, Dec 19 2008

Extensions

Edited by R. J. Mathar, Apr 09 2009

Status

approved