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

0,11

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

Links

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

Formula

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

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A101337.

Sequence in context: A251759 A243087 A123464 * A329562 A069877 A085940

Adjacent sequences: A113016 A113017 A113018 * A113020 A113021 A113022

Keyword

base,easy,nonn

Author

Alexandre Wajnberg, Jan 03 2006

Status

approved