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

%I #10 Nov 09 2019 17:38:17

%S 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,

%T 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,

%U 3,9,9,5,8,6,4,0,2,0,5,5,8,8,0

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

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

%C 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.

%H Stanislav Sykora, <a href="/A260800/b260800.txt">Table of n, a(n) for n = 0..2000</a>

%e 0.87443395094120986641796610477823160007054752616633263886434842992...

%e The negative solution of the equation is -(a+e) =

%e -3.5927157794002551017782535761308940978277946198662922138313160576...

%p evalf((sqrt(exp(2)+4*Pi)-exp(1))/2); # _R. J. Mathar_, Aug 20 2015

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

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

%Y Cf. A000796, A001113, A260799.

%K nonn,cons,easy

%O 0,1

%A _Stanislav Sykora_, Jul 31 2015