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

Author

Stanislav Sykora, Nov 03 2013

Keywords

• nonn
• cons

Examples

			0.685947035167428481875735 ...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000
• Wikipedia, Euler-Mascheroni constant
• Wikipedia, Lambert W function
• Wikipedia, Tetration

Crossrefs

Cf. A001620.

Programs

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 *)

PARI

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

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).