A113009 {Sum of the digits 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, 100, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 36, 49, 64, 81, 100, 121, 144, 169, 196

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, 81, 5832. Are there any others?

Fixed points include: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 81, 512, 2401. There are no other fixed points less than 10^1000. - Chai Wah Wu, Feb 28 2019

Examples

			a(9)=9^1=9
a(19)=(1+9)^2=100
a(101)=(1+0+1)^3=8
		

Crossrefs

Cf. A101337.

Programs

Mathematica

Join[{0},Table[Total[IntegerDigits[n]]^IntegerLength[n],{n,100}]] (* Harvey P. Dale, Nov 09 2014 *)

Python

def A113009(n):
    return sum(int(d) for d in str(n))**len(str(n)) # Chai Wah Wu, Feb 28 2019

Formula

a(ijk...)[m digits ijk...]=(i+j+k)^m