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A376841
Decimal expansion of a constant related to the asymptotics of A066447 and A333374.
3
7, 1, 5, 7, 8, 7, 4, 1, 7, 8, 6, 1, 4, 3, 5, 2, 4, 8, 8, 0, 2, 0, 5, 0, 1, 6, 4, 9, 9, 8, 9, 1, 0, 1, 6, 0, 6, 4, 8, 2, 6, 7, 9, 7, 5, 9, 3, 5, 4, 9, 3, 7, 3, 6, 1, 9, 5, 7, 5, 8, 6, 2, 7, 2, 5, 2, 3, 3, 7, 2, 3, 7, 1, 3, 7, 9, 3, 2, 6, 7, 7, 9, 3, 1, 5, 5, 3, 5, 7, 1, 4, 2, 1, 6, 4, 3, 3, 3, 7, 8, 6, 9, 0, 6, 6
OFFSET
1,1
FORMULA
Equals limit_{n->infinity} A066447(n)^(1/sqrt(n)).
Equals limit_{n->infinity} A333374(n)^(1/sqrt(n)).
Equals exp(2*sqrt(log(r)^2 - polylog(2, -r^2) + polylog(2, r^2))), where r = A192918 = 0.54368901269207636157... is the real root of the equation r^2*(1+r) = 1-r.
EXAMPLE
7.1578741786143524880205016499891016064826797593549373619575862725233...
MATHEMATICA
RealDigits[E^(2*Sqrt[Log[r]^2 + PolyLog[2, r^2] - PolyLog[2, -r^2]]) /. r -> (-1 - 2/(17 + 3*Sqrt[33])^(1/3) + (17 + 3*Sqrt[33])^(1/3))/3, 10, 105][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Oct 06 2024
STATUS
approved