A019798 Decimal expansion of sqrt(2*e).

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, 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, 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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

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

Examples

			2.3316439815971242033635360621684008763802362991875884230...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• Index entries for transcendental numbers.

Crossrefs

Cf. A001113, A019774, A257775, A257776.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2*Exp(1)); // G. C. Greubel, Sep 08 2018

Mathematica

RealDigits[Sqrt[2*E], 10, 100][[1]] (* G. C. Greubel, Sep 08 2018 *)

PARI

sqrt(2*exp(1)) \\ Michel Marcus, Nov 05 2015

Formula

From Amiram Eldar, Jul 08 2023: (Start)

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

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