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
Stanislav Sykora, Table of n, a(n) for n = 1..2000
Stanislav Sykora, PARI/GP script for Tetration Limit.
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