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A231097 Decimal expansion of the power tower of the ratio E/Pi. 1
8, 8, 0, 3, 6, 7, 7, 7, 8, 9, 8, 1, 7, 3, 4, 6, 2, 1, 8, 2, 6, 7, 4, 9, 8, 5, 2, 8, 5, 4, 4, 2, 0, 7, 1, 1, 4, 5, 9, 5, 7, 9, 9, 6, 3, 4, 7, 6, 6, 3, 4, 9, 2, 9, 1, 6, 4, 8, 1, 9, 6, 3, 6, 2, 0, 5, 7, 2, 4, 7, 6, 6, 4, 9, 9, 9, 0, 3, 9, 9, 4, 2, 0, 4, 2, 8, 3, 9, 1, 9, 8, 4, 2, 2, 0, 8, 1, 8, 7, 4, 6, 6, 1, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This infinite tetration limit of (E/Pi)^^n is also the only solution of x*(Pi/E)^x = 1.

LINKS

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

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

0.88036777898173462182674985...

PROG

(PARI) lambertw(log(Pi)-1)/(log(Pi)-1)

CROSSREFS

Cf. A061360 (E/Pi), A231098 (tetration of Pi/E).

Sequence in context: A273818 A179639 A113809 * A243508 A144802 A275477

Adjacent sequences:  A231094 A231095 A231096 * A231098 A231099 A231100

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Nov 06 2013

STATUS

approved

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Last modified August 22 01:16 EDT 2017. Contains 290942 sequences.