login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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...

PROG

(PARI) (sqrt(Pi*Pi+4*exp(1))-Pi)/2

CROSSREFS

Cf. A000796, A001113, A260800.

Sequence in context: A153871 A198934 A119524 * A021590 A094241 A021938

Adjacent sequences:  A260796 A260797 A260798 * A260800 A260801 A260802

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Jul 31 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 26 17:21 EDT 2017. Contains 285449 sequences.