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

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

Sequence in context: A221217 A018868 A302712 * A171537 A200096 A220086

Adjacent sequences: A125086 A125087 A125088 * A125090 A125091 A125092

Keyword

nonn,base

Author

A. Timothy Royappa, Apr 08 2008, Apr 14 2008

Status

approved