cp's OEIS Frontend

A125089 First nonzero digit of solution to log_n(z) = -z, where log_n stands for the base-n logarithm.

%I A125089 #5 Jul 12 2015 16:17:13
%S A125089 6,5,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T A125089 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A125089 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A125089 First nonzero digit of solution to log_n(z) = -z, where log_n stands for the base-n logarithm.
%F A125089 First nonzero digit of W(log(n))/log(n) for integer n > 1. Here W is the Lambert W function.
%e A125089 a(2) = 6 because 6 is the first digit of the solution (z = 0.641...) to the generating equation log_2(z) = -z.
%o A125089 Mathcad program for first 3000 or so terms (substitute an integer > 1 for n): trunc(10*root(log(z,n)+z,z))
%K A125089 nonn,base
%O A125089 2,1
%A A125089 _A. Timothy Royappa_, Apr 08 2008, Apr 14 2008