A376658 Decimal expansion of a constant related to the asymptotics of A376624 and A376625.

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

Offset

1,1

Links

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

Formula

Equals exp(sqrt(2*(log(r)^2 + 2*polylog(2, sqrt(r))))), where r = A072223 = 0.52488859865640479389948613854128391569... is the smallest real root of the equation (1 - r^2)^2 = r.

Equals limit_{n->infinity} A376624(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A376625(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A377075(n)^(1/sqrt(n)).

Equals exp(2*sqrt(2*log(A356032)^2 + polylog(2, A356032))).

Example

8.46018724425296480975230009888917594335470635951014367622821158904321498...

Mathematica

RealDigits[E^(Sqrt[2*Log[r]^2 + 4*PolyLog[2, Sqrt[r]]]) /. r -> 1/(2*Sqrt[3/(4 + ((155 - 3*Sqrt[849])/2)^(1/3) + ((155 + 3*Sqrt[849])/2)^(1/3))]) - Sqrt[8/3 - ((155 - 3*Sqrt[849])/2)^(1/3)/3 - ((155 + 3*Sqrt[849])/2)^(1/3)/3 + 2*Sqrt[3/(4 + ((155 - 3*Sqrt[849])/2)^(1/3) + ((155 + 3*Sqrt[849])/2)^(1/3))]]/2, 10, 105][[1]]

Crossrefs

Cf. A072223, A333198, A376621, A376624, A376625, A376659, A376660, A377075.

Cf. A356032.

Sequence in context: A376875 A021926 A254067 * A178727 A354917 A243446

Adjacent sequences: A376655 A376656 A376657 * A376659 A376660 A376661

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 01 2024

Status

approved