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A231096 Decimal expansion of the power tower of the inverse of golden ratio. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.