1,3

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.

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

Equals LambertW(1-log(Pi))/(1-log(Pi)). - Alois P. Heinz, Jul 12 2018

1.18752363535924990543840790...

(PARI) See the above link

Cf. A000796, A001113.

Sequence in context: A185346 A200017 A316728 * A072003 A160668 A086033

Adjacent sequences: A231095 A231096 A231097 * A231099 A231100 A231101

nonn,cons

Stanislav Sykora, Nov 06 2013

approved