A019798 - OEIS

%I #26 Jul 08 2023 04:06:23

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

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

%U 1,0,0,4,9,4,1,2,6,5,7,3,4,9,5,0,2,6,2,9,9,9,1,7,9,5,4,7,7,7,5

%N Decimal expansion of sqrt(2*e).

%C The coefficient a for which y=a*sqrt(x) kisses the exponential function y=exp(x). The kissing point is (0.5, sqrt(e)). For more details, see A257776. Also, inverse of this constant equals the maximum value of sqrt(x)*exp(-x) for positive x, attained at x=1/2. - _Stanislav Sykora_, Nov 04 2015

%H Ivan Panchenko, <a href="/A019798/b019798.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F From _Amiram Eldar_, Jul 08 2023: (Start)

%F Equals Product_{n>=0} (e / (1 + 1/(n-1/2))^n).

%F Equals Product_{n>=0} (e * (1 - 1/(n+1/2))^n). (End)

%e 2.3316439815971242033635360621684008763802362991875884230...

%t RealDigits[Sqrt[2*E], 10, 100][[1]] (* _G. C. Greubel_, Sep 08 2018 *)

%o (PARI) sqrt(2*exp(1)) \\ _Michel Marcus_, Nov 05 2015

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2*Exp(1)); // _G. C. Greubel_, Sep 08 2018

%Y Cf. A001113, A019774, A257775, A257776.

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_