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A084238 a(2) = 1, and for n > 2 a(n) is the least k such that log(k) < k^(1/n) and log(k-1) >= (k-1)^(1/n). 1
1, 94, 5504, 332106, 24128092, 2099467159, 214910065296, 25438034785805, 3430631121407802, 520643904835474202, 87994213187313363255, 16416338625038083857946, 3355257076845892674934411, 746397968687429806357762425, 179698501514006236611711868382, 46589028541465014633355926255885 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=2..17.

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. - Wong Ching Yin, 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

Sequence in context: A017757 A220759 A218178 * A252769 A218519 A281138

Adjacent sequences:  A084235 A084236 A084237 * A084239 A084240 A084241

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, May 18 2003

EXTENSIONS

a(14)-a(16) from Wong Ching Yin, Feb 26 2021

Name clarified by Pontus von Brömssen, Oct 11 2021

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)