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A260799 Decimal expansion of the continued fraction e/(Pi+e/(Pi+e/(...))). 2
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A365350 A198934 A119524 * A021590 A094241 A021938
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Jul 31 2015
STATUS
approved

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Last modified April 22 08:40 EDT 2024. Contains 371893 sequences. (Running on oeis4.)