A231096 Decimal expansion of the power tower of the inverse of golden ratio.

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

Offset: 0

Author

Stanislav Sykora, Nov 04 2013

Keywords

• nonn
• cons

Comments

Also the only solution of x*phi^x = 1.

Examples

			0.710439287156503188669345...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..1999
• Wikipedia, Lambert W function
• Wikipedia, Tetration

Crossrefs

Cf. A094214 (1/phi), A001622 (phi), A231095 (power tower of Gamma).

Programs

Mathematica

RealDigits[ LambertW[ Log[ GoldenRatio]]/Log[ GoldenRatio], 10, 111][[1]] (* Robert G. Wilson v, Feb 11 2015 *)

PARI

lambertw(log(phi))/log(phi)

Formula

When 1/E^E <= c < 1, then c^c^c^... = LambertW(log(1/c))/log(1/c).