A242760 Decimal expansion of the odd limit of the harmonic power tower (1/2)^(1/3)^...^(1/(2n+1)).

6, 9, 0, 3, 4, 7, 1, 2, 6, 1, 1, 4, 9, 6, 4, 3, 1, 9, 4, 6, 7, 3, 2, 8, 4, 3, 8, 4, 6, 4, 1, 8, 9, 4, 2, 4, 4, 3, 9, 8, 3, 3, 1, 9, 7, 3, 8, 2, 7, 2, 6, 7, 0, 0, 2, 8, 9, 6, 1, 3, 1, 9, 1, 6, 4, 3, 6, 5, 0, 1, 5, 3, 5, 2, 8, 9, 1, 1, 5, 3, 3, 4, 9, 3, 8, 6, 7, 7, 1, 3, 2, 9, 5, 5, 0, 2, 8, 4, 4, 5, 8, 2, 4, 7, 9

Offset

0,1

Comments

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

References

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

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's MathWorld, Power Tower

Example

0.6903471261149643194673284384641894244398...

Mathematica

digits = 40; dn = 10; $RecursionLimit = 1000; Clear[h]; h[n_] := h[n] = Power @@ (1/Range[2, n]); h[dn + 1]; h[n = 2*dn + 1]; 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 + 1), 1000]; Do[s = 1/m^s, {m, 2*n, 2, -1}]; difs = s - sold; sold = s; n++]; RealDigits[s, 10, 120][[1]] (* Vaclav Kotesovec, Feb 17 2021 *)

Crossrefs

Cf. A242759.

Sequence in context: A198118 A195102 A020792 * A196607 A200015 A298517

Adjacent sequences: A242757 A242758 A242759 * A242761 A242762 A242763

Keyword

nonn,cons

Author

Jean-François Alcover, May 22 2014

Extensions

More terms from Alois P. Heinz, May 22 2014

Status

approved