A376152 Decimal expansion of a constant related to the asymptotics of A376530.

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

Offset: 1

Author

Vaclav Kotesovec, Oct 09 2024

Keywords

• nonn
• cons

Examples

			4.988020876600903805335224460790773050832038156091687962387444991919...
		

Crossrefs

Cf. A376530, A376621.

Programs

Mathematica

RealDigits[E^(2*Sqrt[Log[r]^2 + 2*PolyLog[2, 1-r] - 2*PolyLog[2, 1-r^3]/3]) /. r -> (-1 - 2/(17 + 3*Sqrt[33])^(1/3) + (17 + 3*Sqrt[33])^(1/3))/3, 10, 120][[1]]

Formula

Equals limit_{n->infinity} A376530(n)^(1/sqrt(n)).

Equals exp(2*sqrt(log(r)^2 + 2*polylog(2, 1-r) - 2*polylog(2, 1-r^3)/3)), where r = A192918 = 0.54368901269207636157085597180174... is the real root of the equation r^2 * (1-r^3)^2 = (1-r)^2.