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A231098 Decimal expansion of the power tower of the ratio Pi/e. 2


%S 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,

%T 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,

%U 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

%N Decimal expansion of the power tower of the ratio Pi/e.

%C 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.

%H Stanislav Sykora, <a href="/A231098/b231098.txt">Table of n, a(n) for n = 1..2000</a>

%H Stanislav Sykora, <a href="https://oeis.org/wiki/File:TetrationLimit.txt">PARI/GP script for Tetration Limit</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration">Tetration</a>

%F Equals LambertW(1-log(Pi))/(1-log(Pi)). - _Alois P. Heinz_, Jul 12 2018

%e 1.18752363535924990543840790...

%o (PARI) See the above link

%Y Cf. A000796, A001113.

%K nonn,cons

%O 1,3

%A _Stanislav Sykora_, Nov 06 2013

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Last modified June 18 03:46 EDT 2021. Contains 345098 sequences. (Running on oeis4.)