A098584 Limit of the power tower t(2)^(t(3)^(t(4)^(t(5)^(...) ...))) in which t(n)=n^(1/n!).

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

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 16 2004

Keywords

• cons
• easy
• nonn

Examples

			1.523230324208529830704308172517706557622863529177583804423211462834333571897662804971965924543364193...
		

Crossrefs

See A098454 for the limit if t(n)=n^(1/n).

Programs

Maple

m:=1: for n from 300 to 2 by -1 do: m:=(n^(1/n!))^m: od: evalf(m,100);

Mathematica

f[n_] := Block[{k = n, e = 1}, While[k > 1, e = N[(k^(1/k!))^e, 128]; k-- ]; e]; RealDigits[ f[18], 10, 105][[1]] (* Robert G. Wilson v, Sep 18 2004 *)