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

Author

Cino Hilliard, Dec 31 2004

Keywords

• easy
• nonn
• base

Comments

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

Examples

			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
		

Links

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

Crossrefs

Cf. A000400, A001024, A007953, A009968, A009977, A009986, A010888, A100401, A159991.

Programs

Mathematica

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

PARI

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

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

a(n) = A007953(6*a(n-1)) = A010888(6*a(n-1)). - Stefano Spezia, Mar 20 2025