Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Jul 12 2015 16:17:13
%S 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 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 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 First nonzero digit of solution to log_n(z) = -z, where log_n stands for the base-n logarithm.
%F First nonzero digit of W(log(n))/log(n) for integer n > 1. Here W is the Lambert W function.
%e a(2) = 6 because 6 is the first digit of the solution (z = 0.641...) to the generating equation log_2(z) = -z.
%o Mathcad program for first 3000 or so terms (substitute an integer > 1 for n): trunc(10*root(log(z,n)+z,z))
%K nonn,base
%O 2,1
%A _A. Timothy Royappa_, Apr 08 2008, Apr 14 2008