OFFSET
1,2
FORMULA
Let b(n)=n^(1/n). Let m=1, initially. For values of k from n to 2 in steps of -1, calculate m -> b(k)^m. This leads to the approximation of the constant starting at n^(1/n). The constant is the limit as n -> infinity.
EXAMPLE
1.941461123582071691514948378198126204362968920678316646300839656299146919...
MAPLE
a:=array(2..150): a[2]:=2^(1/2): for n from 3 to 150 do: m:=1: for p from n to 2 by -1 do: m:=(p^(1/p))^m: od: a[n]:=m: od: evalf(a[150], 100);
MATHEMATICA
f[n_] := Block[{k = n, e = 1}, While[k > 1, e = N[(k^(1/k))^e, 128]; k-- ]; e]; RealDigits[ f[105], 10, 105][[1]] (* Robert G. Wilson v, Sep 10 2004 *)
CROSSREFS
KEYWORD
AUTHOR
Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004
EXTENSIONS
More terms from Robert G. Wilson v, Sep 10 2004
Offset corrected by R. J. Mathar, Feb 05 2009
STATUS
approved