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

1,1

Links

Table of n, a(n) for n=1..105.

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.

Example

4.988020876600903805335224460790773050832038156091687962387444991919...

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]]

Crossrefs

Cf. A376530, A376621.

Sequence in context: A081382 A188658 A248803 * A019784 A276539 A011381

Adjacent sequences: A376149 A376150 A376151 * A376153 A376154 A376155

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 09 2024

Status

approved