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

0,1

Comments

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

Links

Stanislav Sykora, Table of n, a(n) for n = 0..1999

Wikipedia, Lambert W function

Wikipedia, Tetration

Formula

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

Example

0.710439287156503188669345...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A256778 A218620 A195911 * A240907 A179376 A152447

Adjacent sequences: A231093 A231094 A231095 * A231097 A231098 A231099

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 04 2013

Status

approved