A376659 - OEIS

A376659

Decimal expansion of a constant related to the asymptotics of A376626 and A376627.

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

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OFFSET

1,1

LINKS

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

FORMULA

Equals exp(sqrt(2*(3*log(r)^2 + polylog(2, 1 - r^2)))), where r = A075778 = 0.7548776662466927600495088963585286918946... is the real root of the equation r^2*(1+r) = 1.

Equals limit_{n->infinity} A376626(n)^(1/sqrt(n)).

Equals limit_{n->infinity} A376627(n)^(1/sqrt(n)).

EXAMPLE

3.33526020703708086029122448156335246730884987099277968...

MATHEMATICA

RealDigits[E^Sqrt[6*Log[r]^2 + 2*PolyLog[2, 1 - r^2]] /. r -> (-1 + ((25 - 3*Sqrt[69])/2)^(1/3) + ((25 + 3*Sqrt[69])/2)^(1/3))/3, 10, 105][[1]]

CROSSREFS

Cf. A075778, A333198, A376621, A376626, A376627, A376658, A376660.

Sequence in context: A285286 A123371 A011277 * A084742 A242033 A375848

Adjacent sequences: A376656 A376657 A376658 * A376660 A376661 A376662

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Oct 01 2024

STATUS

approved