|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|