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