A242759 Decimal expansion of the even limit of the harmonic power tower (1/2)^(1/3)^...^(1/(2n)).

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, 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, 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

Offset: 0

Author

Jean-François Alcover, May 22 2014

Keywords

• nonn
• cons

Comments

The harmonic power tower sequence is divergent in the sense that even and odd partial exponentials converge to distinct limits. [after Steven Finch]

Examples

			0.6583655992663311881846549513080943690418...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.11, p. 449.

Links

• Eric Weisstein's MathWorld, Power Tower

Crossrefs

Cf. A242760.

Programs

Mathematica

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
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 *)

Extensions

More terms from Alois P. Heinz, May 22 2014