A376841 Decimal expansion of a constant related to the asymptotics of A066447 and A333374.

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

Offset: 1

Author

Vaclav Kotesovec, Oct 06 2024

Keywords

• nonn
• cons

Examples

			7.1578741786143524880205016499891016064826797593549373619575862725233...
		

Crossrefs

Cf. A066447, A192918, A333374.

Programs

Mathematica

RealDigits[E^(2*Sqrt[Log[r]^2 + PolyLog[2, r^2] - PolyLog[2, -r^2]]) /. r -> (-1 - 2/(17 + 3*Sqrt[33])^(1/3) + (17 + 3*Sqrt[33])^(1/3))/3, 10, 105][[1]]

Formula

Equals limit_{n->infinity} A066447(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A333374(n)^(1/sqrt(n)).

Equals exp(2*sqrt(log(r)^2 - polylog(2, -r^2) + polylog(2, r^2))), where r = A192918 = 0.54368901269207636157... is the real root of the equation r^2*(1+r) = 1-r.