A100403 Digital root of 6^n.

1, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset

0,2

Comments

Also the digital root of k^n for any k == 6 (mod 9). - Timothy L. Tiffin, Dec 02 2023

Links

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

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

Formula

From Timothy L. Tiffin, Dec 01 2023: (Start)

a(n) = 9 for n >= 2.

G.f.: (1+5x+3x^2)/(1-x).

a(n) = A100401(n) for n <> 1.

a(n) = A010888(A000400(n)) = A010888(A001024(n)) = A010888(A009968(n)) = A010888(A009977(n)) = A010888(A009986(n)) = A010888(A159991(n)). (End)

E.g.f.: 9*exp(x) - 3*x - 8. - Elmo R. Oliveira, Aug 09 2024

Example

For n=8, the digits of 6^8 = 1679616 sum to 36, whose digits sum to 9. So, a(8) = 9. - Timothy L. Tiffin, Dec 01 2023

Mathematica

PadRight[{1, 6}, 100, 9] (* Timothy L. Tiffin, Dec 03 2023 *)

Prog

(PARI) a(n) = if( n<2, [1, 6][n+1], 9); \\ Joerg Arndt, Dec 03 2023

Crossrefs

Cf. A000400, A001024, A009968, A009977, A009986, A010888, A100401, A159991.

Sequence in context: A195296 A273951 A307053 * A066002 A140052 A316072

Adjacent sequences: A100400 A100401 A100402 * A100404 A100405 A100406

Keyword

easy,nonn,base

Author

Cino Hilliard, Dec 31 2004

Status

approved