A260800 Decimal expansion of (sqrt(e*e+4*Pi)-e)/2.

8, 7, 4, 4, 3, 3, 9, 5, 0, 9, 4, 1, 2, 0, 9, 8, 6, 6, 4, 1, 7, 9, 6, 6, 1, 0, 4, 7, 7, 8, 2, 3, 1, 6, 0, 0, 0, 7, 0, 5, 4, 7, 5, 2, 6, 1, 6, 6, 3, 3, 2, 6, 3, 8, 8, 6, 4, 3, 4, 8, 4, 2, 9, 9, 2, 9, 8, 6, 3, 9, 9, 5, 8, 6, 4, 0, 2, 0, 5, 5, 8, 8, 0

Offset

0,1

Comments

Also the decimal expansion of the 2-periodic continued fraction Pi/(e+Pi/(e+Pi/(...))).

Also the positive solution of the equation x*(x+e)=Pi, and the unique attractor of the real mapping M(x)=Pi/(e+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

Example

0.87443395094120986641796610477823160007054752616633263886434842992...
The negative solution of the equation is -(a+e) =
-3.5927157794002551017782535761308940978277946198662922138313160576...

Maple

evalf((sqrt(exp(2)+4*Pi)-exp(1))/2); # R. J. Mathar, Aug 20 2015

Mathematica

RealDigits[(Sqrt[E^2+4Pi]-E)/2, 10, 120][[1]] (* Harvey P. Dale, Nov 09 2019 *)

Prog

(PARI) e=exp(1); a=(sqrt(e*e+4*Pi)-e)/2

Crossrefs

Cf. A000796, A001113, A260799.

Sequence in context: A193716 A268046 A260060 * A196914 A072102 A274442

Adjacent sequences: A260797 A260798 A260799 * A260801 A260802 A260803

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Jul 31 2015

Status

approved