A340168 Decimal expansion of a constant related to the asymptotics of A004003.

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

Offset: 1

Author

Vaclav Kotesovec, Dec 30 2020

Keywords

• nonn
• cons

Examples

			1.1088622587807675132769511621308192926452661269635692243629431418447355653...
		

Crossrefs

Cf. A004003, A007341, A007726, A065072, A127605, A340052.

Programs

Mathematica

RealDigits[2*E^(Catalan/Pi)/(1 + Sqrt[2]), 10, 110][[1]]

Formula

Equals lim_{n->infinity} A004003(n) / ((sqrt(2)-1)^(2*n) * exp(4*G*n*(n+1)/Pi)), where G is the Catalan's constant A006752.

Equals 2*exp(G/Pi) / (1 + sqrt(2)), where G is Catalan's constant A006752.