A125089 - OEIS

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A125089

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

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, 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, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

LINKS

Table of n, a(n) for n=2..106.

FORMULA

First nonzero digit of W(log(n))/log(n) for integer n > 1. Here W is the Lambert W function.

EXAMPLE

a(2) = 6 because 6 is the first digit of the solution (z = 0.641...) to the generating equation log_2(z) = -z.

PROG

Mathcad program for first 3000 or so terms (substitute an integer > 1 for n): trunc(10*root(log(z, n)+z, z))

CROSSREFS