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%I #7 Jul 26 2015 01:32:24
%S 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,
%T 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,
%U 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
%N 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.
%F 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.
%e 1.941461123582071691514948378198126204362968920678316646300839656299146919...
%p 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);
%t 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 *)
%K cons,easy,nonn
%O 1,2
%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004
%E More terms from _Robert G. Wilson v_, Sep 10 2004
%E Offset corrected by _R. J. Mathar_, Feb 05 2009
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