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%I #9 May 25 2023 03:09:30
%S 7,0,6,4,1,3,1,3,4,0,8,7,3,0,0,0,6,9,2,7,4,1,4,3,9,4,6,1,3,9,5,0,0,2,
%T 5,5,3,3,5,7,0,6,0,8,1,2,1,9,5,2,1,1,1,4,5,8,2,4,1,5,8,6,6,8,8,3,3,7,
%U 6,1,5,3,4,4,0,2,2,7,2,3,7,0,6,0,2,5,3,9,0,1,7,9,9,2,6,3,6,6,6,1,8,4,7,0,0
%N Decimal expansion of the continued fraction e/(Pi+e/(Pi+e/(...))).
%C Also the positive solution of the equation x*(x+Pi)=e, and the unique attractor of the real mapping M(x)=e/(Pi+x), with e being the Euler number. The negative solution of the equation is an invariant point, but not an attractor, of M(x) and does not lead to a convergent c.f.
%H Stanislav Sykora, <a href="/A260799/b260799.txt">Table of n, a(n) for n = 0..2000</a>
%F Equals (sqrt(Pi*Pi+4*e)-Pi)/2.
%e 0.706413134087300069274143946139500255335706081219521114582415866883...
%e The negative solution of the equation is -(a+Pi) =
%e -3.84800578767709330773678732941900313953287548059462693555736045919...
%t RealDigits[(Sqrt[Pi^2 + 4*E] - Pi)/2, 10, 120][[1]] (* _Amiram Eldar_, May 25 2023 *)
%o (PARI) (sqrt(Pi*Pi+4*exp(1))-Pi)/2
%Y Cf. A000796, A001113, A260800.
%K nonn,cons
%O 0,1
%A _Stanislav Sykora_, Jul 31 2015
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