OFFSET
2,2
COMMENTS
A demonstration "that log x increases slower than any power of x. ... No matter how small you make a, the graph of log x is eventually flatter than the graph of x^a."
REFERENCES
John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Joseph Henry Press, Washington, D.C., 2003, Page 72 - 75.
FORMULA
For n = 1, a(n) = 1. For n>=2, a(n) = ceiling(e^(-(n+1)*W-1(-1/(n+1)))) where W-1(x) is the Lambert W function with branch -1. - Joseph C. Y. Wong, Feb 26 2021
MATHEMATICA
Table[ Floor[ FindRoot[ Log[x]^n == x, {x, 10^(2n)}, AccuracyGoal -> 24, WorkingPrecision -> 34][[1, 2]] + 1], {n, 2, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, May 18 2003
EXTENSIONS
a(14)-a(16) from Joseph C. Y. Wong, Feb 26 2021
Name clarified by Pontus von Brömssen, Oct 11 2021
STATUS
approved