A376660 Decimal expansion of a constant related to the asymptotics of A376630 and A376631.

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

Offset

1,1

Links

Table of n, a(n) for n=1..106.

Formula

Equals limit_{n->infinity} A376630(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A376631(n)^(1/sqrt(n)).

Equals A376815^(1/2). - Vaclav Kotesovec, Oct 06 2024

Equals exp(sqrt(3*log(r)^2/4 + 2*polylog(2, r^(1/2)) - Pi^2/6)), where r = A088559 = 0.4655712318767680266567312252199... is the real root of the equation r*(1+r)^2 = 1. - Vaclav Kotesovec, Oct 07 2024

Example

2.045390691852050639893704244342601252265948793467833187994662870934455617...

Mathematica

RealDigits[E^Sqrt[3*Log[r]^2/4 + 2*PolyLog[2, r^(1/2)] - Pi^2/6] /. r -> (-2 + ((29 - 3*Sqrt[93])/2)^(1/3) + ((29 + 3*Sqrt[93])/2)^(1/3))/3, 10, 120][[1]] (* Vaclav Kotesovec, Oct 07 2024 *)

Crossrefs

Cf. A333198, A376621, A376630, A376631, A376658, A376659, A376815.

Cf. A088559.

Sequence in context: A201837 A326052 A004482 * A329233 A111677 A326186

Adjacent sequences: A376657 A376658 A376659 * A376661 A376662 A376663

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 01 2024

Status

approved