A098454 Limit of the power tower defined as follows: 2^(1/2); (2^(1/2))^(3^(1/3)); (2^(1/2))^((3^(1/3))^(4^(1/4))); etc.

1, 9, 4, 1, 4, 6, 1, 1, 2, 3, 5, 8, 2, 0, 7, 1, 6, 9, 1, 5, 1, 4, 9, 4, 8, 3, 7, 8, 1, 9, 8, 1, 2, 6, 2, 0, 4, 3, 6, 2, 9, 6, 8, 9, 2, 0, 6, 7, 8, 3, 1, 6, 6, 4, 6, 3, 0, 0, 8, 3, 9, 6, 5, 6, 2, 9, 9, 1, 4, 6, 9, 1, 9, 3, 1, 7, 4, 1, 9, 9, 1, 6, 2, 2, 8, 5, 0, 6, 0, 6, 3, 3, 0, 1, 7, 2, 5, 8, 5, 4, 0, 8, 4, 1, 8

Offset

1,2

Links

Table of n, a(n) for n=1..105.

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

Sequence in context: A336274 A286229 A242611 * A298531 A154206 A349624

Adjacent sequences: A098451 A098452 A098453 * A098455 A098456 A098457

Keyword

cons,easy,nonn

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