A113018 {Digital root of n} raised to the power {number of digits of n}.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1

Offset: 0

Author

Alexandre Wajnberg, Jan 03 2006

Keywords

• base
• easy
• nonn

Comments

Fixed points are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 81.

Examples

			a(9) = 9^1 = 9;
a(19) = (1 + 9 = 10 => 1 + 0) = 1^2 =  1;
a(85) = (8 + 5 = 13 => 1 + 3) = 4^2 = 16.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A010888, A055642.

Cf. A101337, A113019.

Programs

Maple

A113018 := proc(n) if(n=0)then return 0:fi: return (((n-1) mod 9) + 1)^length(n): end: seq(A113018(n), n=0..100); # Nathaniel Johnston, May 05 2011

Mathematica

Join[{0},Table[ResourceFunction["AdditiveDigitalRoot"][n]^IntegerLength[n],{n,73}]] (* James C. McMahon, Jun 14 2024 *)

Formula

a(n) = A010888(n)^A055642(n). - Michel Marcus, Feb 10 2019