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 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. 5
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified August 5 05:23 EDT 2024. Contains 374935 sequences. (Running on oeis4.)