A113019 (Number of digits of n) raised to the power of (the digital root of n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32

Offset: 0

Author

Alexandre Wajnberg, Jan 03 2006

Keywords

• base
• easy
• nonn

Comments

n=1 and 32 are fixed points. Are there any others?

First occurrence of k: 1,10,100,11,10000,100000,1000000,12,101,1000000000, ..., . - Robert G. Wilson v

Examples

			a(0) = 1^0 = 1.
a(9) = 1^9 = 1.
a(10) = 2^(1+0) = 2.
a(89) = 2^(8+9=17=>1+7) = 2^8 = 256.
		

Links

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

Crossrefs

Cf. A101337.

Programs

Maple

A113019 := proc(n) if(n=0)then return 1:fi: return length(n)^(((n-1) mod 9) + 1): end: seq(A113019(n),n=0..100); # Nathaniel Johnston, May 04 2011

Mathematica

f[n_] := If[n == 0, 1, Floor[ Log[10, 10n]]^(Mod[n - 1, 9] + 1)]; Table[ f[n], {n, 0, 73}] (* Robert G. Wilson v, Jan 04 2006 *)

PARI

apply( A113019(n)=(logint(n+!n,10)+1)^((n-1)%9+1), [0..99]) \\ M. F. Hasler, Nov 17 2019

Formula

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

a(n)=A055642(n)^A010888(n). - Robert G. Wilson v