A333198 - OEIS

A333198

Decimal expansion of a constant related to the asymptotics of A306734 and A333179.

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

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OFFSET

1,2

LINKS

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

FORMULA

Equals limit_{n->infinity} A306734(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A333179(n)^(1/sqrt(n)).

Equals exp(sqrt(4*log(r)^2/3 + 4*polylog(2, 1-r) - Pi^2/3)), where r = 1 - A357471 = 0.4301597090019467340886... is the real root of the equation r^2 = (1-r)^3. - Vaclav Kotesovec, Oct 07 2024

EXAMPLE

1.86429525435844065924747599856112246877295244507368421574403...

MATHEMATICA

RealDigits[E^Sqrt[4*Log[r]^2/3 + 4*PolyLog[2, 1-r] - Pi^2/3] /. r -> (2 - 5*(2/(-11 + 3*Sqrt[69]))^(1/3) + ((-11 + 3*Sqrt[69])/2)^(1/3))/3, 10, 120][[1]] (* Vaclav Kotesovec, Oct 07 2024 *)

CROSSREFS

Cf. A306734, A333179, A333180, A333181, A357471, A376621.

Sequence in context: A343275 A177154 A059631 * A093019 A175573 A296494

Adjacent sequences: A333195 A333196 A333197 * A333199 A333200 A333201

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Mar 11 2020

EXTENSIONS

More digits from Vaclav Kotesovec, Oct 07 2024

STATUS

approved