A231095 Decimal expansion of the power tower of Euler constant gamma.

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

Offset

0,1

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Wikipedia, Euler-Mascheroni constant

Wikipedia, Lambert W function

Wikipedia, Tetration

Formula

In general, for 1/E^E <= c < 1, c^c^c^... = LambertW(log(1/c))/log(1/c). Hence, this number is LambertW(log(1/gamma))/log(1/gamma).

Example

0.685947035167428481875735 ...

Maple

evalf(-LambertW(-log(gamma))/log(gamma), 120); # Vaclav Kotesovec, Oct 26 2014

Mathematica

c = EulerGamma; RealDigits[ ProductLog[-Log[c]]/Log[c], 10, 111] (* Robert G. Wilson v, Oct 24 2014 *)

Prog

(PARI) -lambertw(-log(Euler))/log(Euler)

Crossrefs

Cf. A001620.

Sequence in context: A319032 A344125 A073462 * A201195 A266092 A143627

Adjacent sequences: A231092 A231093 A231094 * A231096 A231097 A231098

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 03 2013

Status

approved