OFFSET
0,1
COMMENTS
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.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..2000
FORMULA
Equals (sqrt(Pi*Pi+4*e)-Pi)/2.
EXAMPLE
0.706413134087300069274143946139500255335706081219521114582415866883...
The negative solution of the equation is -(a+Pi) =
-3.84800578767709330773678732941900313953287548059462693555736045919...
MATHEMATICA
RealDigits[(Sqrt[Pi^2 + 4*E] - Pi)/2, 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)
PROG
(PARI) (sqrt(Pi*Pi+4*exp(1))-Pi)/2
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Jul 31 2015
STATUS
approved