A332915 Decimal expansion of the constant W(1) + 1/W(1), where W is Lambert's function.

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

Offset: 1

Author

Martin Renner, Mar 02 2020

Keywords

• nonn
• cons

Comments

The graph of the exponential function exp(x) moved to the right by W(1) + 1/W(1) touches the graph of the natural logarithm log(x) at point (x,y) = (1/W(1), W(1)) = (A030797, A030178).

Examples

			2.33036612476168058322517043916206263018983377385398...
		

Crossrefs

Cf. A030178, A030797, A052888.

Programs

Maple

evalf[200](LambertW(1) + 1/LambertW(1));

Mathematica

RealDigits[N[LambertW[1] + 1/LambertW[1], 120]][[1]] (* Vaclav Kotesovec, Mar 02 2020 *)

PARI

my(x=lambertw(1)); x+1/x \\ Michel Marcus, Mar 02 2020

Formula

Equals A030178 + A030797 = A030178 + 1/A030178 = 1/A030797 + A030797.

Equals 2 + Integral_{x=0..1} W(x) dx. - Amiram Eldar, Jul 18 2021