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A125089
First nonzero digit of solution to log_n(z) = -z, where log_n stands for the base-n logarithm.
0
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
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
KEYWORD
nonn,base
AUTHOR
A. Timothy Royappa, Apr 08 2008, Apr 14 2008
STATUS
approved