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A098454
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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.
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5
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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
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..105.
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FORMULA
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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.
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EXAMPLE
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1.941461123582071691514948378198126204362968920678316646300839656299146919...
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MAPLE
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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);
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MATHEMATICA
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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]] (from Robert G. Wilson v Sep 10 2004)
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CROSSREFS
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Sequence in context: A112146 A056897 A010158 * A154206 A094881 A019751
Adjacent sequences: A098451 A098452 A098453 * A098455 A098456 A098457
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004
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EXTENSIONS
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More terms from Robert G. Wilson v, Sep 10 2004
Offset corrected by R. J. Mathar, Feb 05 2009
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STATUS
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approved
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