OFFSET
0,1
COMMENTS
Fredrik Johansson remarks: "The inequality log(1 + x) <= x is used all the time. Putting x^a on the right gives a bound that grows less quickly and which remains easy to manipulate multiplicatively."
EXAMPLE
0.37983121492661090182261...
MAPLE
Digits := 120: Optimization:-Maximize(log(log(1 + x))/log(x), {x>=9})[1]:
evalf(%)*10^105: ListTools:-Reverse(convert(floor(%), base, 10));
MATHEMATICA
RealDigits[FindMaximum[Log[Log[1 + x]]/Log[x], {x, 7}, WorkingPrecision -> 110][[1]], 10, 105][[1]] (* Amiram Eldar, Oct 16 2021 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Peter Luschny, Oct 16 2021
STATUS
approved