login
A231097
Decimal expansion of the power tower of the ratio e/Pi.
2
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
OFFSET
0,1
COMMENTS
This infinite tetration limit of (e/Pi)^^n is also the only solution of x*(Pi/e)^x = 1.
LINKS
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...
MATHEMATICA
RealDigits[ProductLog[Log[Pi] - 1]/(Log[Pi] - 1), 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)
PROG
(PARI) lambertw(log(Pi)-1)/(log(Pi)-1)
CROSSREFS
Cf. A061360 (e/Pi), A231098 (tetration of Pi/e).
Sequence in context: A326802 A179639 A113809 * A309820 A309826 A321096
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, Nov 06 2013
STATUS
approved