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A231098
Decimal expansion of the power tower of the ratio Pi/e.
2
1, 1, 8, 7, 5, 2, 3, 6, 3, 5, 3, 5, 9, 2, 4, 9, 9, 0, 5, 4, 3, 8, 4, 0, 7, 9, 0, 2, 8, 2, 3, 6, 3, 2, 7, 7, 3, 2, 9, 2, 4, 0, 6, 0, 5, 3, 1, 2, 1, 9, 5, 2, 3, 7, 8, 9, 0, 6, 0, 3, 1, 3, 6, 5, 9, 4, 3, 5, 0, 0, 0, 4, 5, 1, 8, 6, 6, 2, 3, 8, 3, 7, 7, 5, 9, 3, 0, 3, 4, 9, 9, 0, 4, 7, 6, 8, 2, 2, 8, 1, 5, 8, 2, 0, 1
OFFSET
1,3
COMMENTS
This limit for n->infinity of the tetration (Pi/e)^^n exists because Pi/e < e^(1/e). Its value is also the smaller one of the two solutions of x*(e/Pi)^x = 1.
LINKS
Wikipedia, Lambert W function.
Wikipedia, Tetration.
FORMULA
Equals LambertW(1-log(Pi))/(1-log(Pi)). - Alois P. Heinz, Jul 12 2018
EXAMPLE
1.18752363535924990543840790...
MATHEMATICA
RealDigits[ProductLog[1 - Log[Pi]]/(1 - Log[Pi]), 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)
PROG
(PARI) See the above link
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Nov 06 2013
STATUS
approved