cp's OEIS Frontend

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

%I A113018 #19 Jun 14 2024 11:35:54
%S A113018 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,
%T A113018 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,
%U A113018 81,1,4,9,16,25,36,49,64,81,1,4,9,16,25,36,49,64,81,1
%N A113018 {Digital root of n} raised to the power {number of digits of n}.
%C A113018 Fixed points are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 81.
%H A113018 Nathaniel Johnston, <a href="/A113018/b113018.txt">Table of n, a(n) for n = 0..10000</a>
%F A113018 a(n) = A010888(n)^A055642(n). - _Michel Marcus_, Feb 10 2019
%e A113018 a(9) = 9^1 = 9;
%e A113018 a(19) = (1 + 9 = 10 => 1 + 0) = 1^2 =  1;
%e A113018 a(85) = (8 + 5 = 13 => 1 + 3) = 4^2 = 16.
%p A113018 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
%t A113018 Join[{0},Table[ResourceFunction["AdditiveDigitalRoot"][n]^IntegerLength[n],{n,73}]] (* _James C. McMahon_, Jun 14 2024 *)
%Y A113018 Cf. A010888, A055642.
%Y A113018 Cf. A101337, A113019.
%K A113018 base,easy,nonn
%O A113018 0,3
%A A113018 _Alexandre Wajnberg_, Jan 03 2006