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A231097 Decimal expansion of the power tower of the ratio E/Pi. 1


%S 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,

%T 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,

%U 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

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

%C This infinite tetration limit of (E/Pi)^^n is also the only solution of x*(Pi/E)^x = 1.

%H Stanislav Sykora, <a href="/A231097/b231097.txt">Table of n, a(n) for n = 0..2000</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 When 1/E^E <= c < 1, then c^c^c^... = LambertW(log(1/c))/log(1/c).

%e 0.88036777898173462182674985...

%o (PARI) lambertw(log(Pi)-1)/(log(Pi)-1)

%Y Cf. A061360 (E/Pi), A231098 (tetration of Pi/E).

%K nonn,cons,easy

%O 0,1

%A _Stanislav Sykora_, Nov 06 2013

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Last modified June 13 15:33 EDT 2021. Contains 345008 sequences. (Running on oeis4.)