A376621 Decimal expansion of a constant related to the asymptotics of A369557 and A376580.

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

Offset

1,1

Links

Table of n, a(n) for n=1..103.

Formula

Equals limit_{n->infinity} A369557(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A376580(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A376542(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A376623(n)^(1/sqrt(n)).

Equals exp(sqrt(3*log(r)^2/2 + 4*polylog(2, r^(1/2)) - Pi^2/3)), where r = A088559 = 0.465571231876768026656731... is the real root of the equation r*(1+r)^2 = 1. - Vaclav Kotesovec, Oct 07 2024

Example

2.75108509088891993943420496204894703641817860263717...

Mathematica

RealDigits[E^Sqrt[3*Log[r]^2/2 + 4*PolyLog[2, r^(1/2)] - Pi^2/3] /. 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, A369557, A376542, A376580, A376623, A376658, A376659, A376660.

Cf. A088559.

Sequence in context: A326098 A198672 A306767 * A113814 A059038 A244678

Adjacent sequences: A376618 A376619 A376620 * A376622 A376623 A376624

Keyword

nonn,cons,new

Author

Vaclav Kotesovec, Sep 30 2024

Status

approved