A098584 - OEIS

%I #4 Jul 28 2015 21:47:52

%S 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,

%T 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,

%U 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

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

%e 1.523230324208529830704308172517706557622863529177583804423211462834333571897662804971965924543364193...

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

%t 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 *)

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

%K cons,easy,nonn

%O 1,2

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