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%I #8 Feb 17 2021 10:16:04
%S 6,5,8,3,6,5,5,9,9,2,6,6,3,3,1,1,8,8,1,8,4,6,5,4,9,5,1,3,0,8,0,9,4,3,
%T 6,9,0,4,1,8,0,0,9,2,6,6,3,8,9,2,8,8,8,6,8,4,1,6,1,0,3,8,3,5,5,1,1,3,
%U 9,3,4,8,3,7,1,8,2,6,2,1,3,4,0,4,0,3,1,8,7,7,8,0,9,8,0,6,5,4,3,1,6,3,5,9,2
%N Decimal expansion of the even limit of the harmonic power tower (1/2)^(1/3)^...^(1/(2n)).
%C The harmonic power tower sequence is divergent in the sense that even and odd partial exponentials converge to distinct limits. [after Steven Finch]
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.11, p. 449.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%e 0.6583655992663311881846549513080943690418...
%t digits = 40; dn = 10; $RecursionLimit = 1000; Clear[h]; h[n_] := h[n] = Power @@ (1/Range[2, n]); h[dn]; h[n = 2*dn]; While[RealDigits[h[n], 10, digits] != RealDigits[h[n - dn], 10, digits], Print["n = ", n]; n = n + dn]; RealDigits[h[n], 10, digits] // First
%t digits = 120; difs = 1; sold = 0; n = 100; While[Abs[difs] > 10^(-digits - 5), s = N[1/(2 n), 1000]; Do[s = 1/m^s, {m, 2 n - 1, 2, -1}]; difs = s - sold; sold = s; n++]; RealDigits[s, 10, 120][[1]] (* _Vaclav Kotesovec_, Feb 17 2021 *)
%Y Cf. A242760.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, May 22 2014
%E More terms from _Alois P. Heinz_, May 22 2014
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