|
Search: id:A084238
|
|
|
| A084238 |
|
Least k such than log(k) < k^(1/n). |
|
+0
1
|
|
| 1, 94, 5504, 332106, 24128092, 2099467159, 214910065296, 25438034785805, 3430631121407802, 520643904835474202, 87994213187313363255, 16416338625038083857946, 3355257076845892674934411
(list; graph; listen)
|
|
|
OFFSET
|
2,2
|
|
|
COMMENT
|
A demonstration "that log x increases slower than any power of x. ... [n]o matter how small you make a, the graph of log x is eventually flatter than the graph of x^a. If a is bigger than 1/e, this is true already[.]"
|
|
REFERENCES
|
John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Joseph Henry Press, Washington, D.C., 2003, Page 72 - 75.
|
|
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: A017810 A035742 A017757 this_sequence A127457 A093007 A033415
Adjacent sequences: A084235 A084236 A084237 this_sequence A084239 A084240 A084241
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), May 18 2003
|
|
|
Search completed in 0.002 seconds
|
