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A376152
Decimal expansion of a constant related to the asymptotics of A376530.
1
4, 9, 8, 8, 0, 2, 0, 8, 7, 6, 6, 0, 0, 9, 0, 3, 8, 0, 5, 3, 3, 5, 2, 2, 4, 4, 6, 0, 7, 9, 0, 7, 7, 3, 0, 5, 0, 8, 3, 2, 0, 3, 8, 1, 5, 6, 0, 9, 1, 6, 8, 7, 9, 6, 2, 3, 8, 7, 4, 4, 4, 9, 9, 1, 9, 1, 9, 5, 5, 2, 9, 6, 5, 3, 4, 2, 1, 0, 1, 1, 8, 3, 9, 2, 4, 3, 7, 9, 6, 0, 7, 2, 5, 7, 7, 9, 8, 0, 7, 3, 9, 0, 8, 5, 1
OFFSET
1,1
FORMULA
Equals limit_{n->infinity} A376530(n)^(1/sqrt(n)).
Equals exp(2*sqrt(log(r)^2 + 2*polylog(2, 1-r) - 2*polylog(2, 1-r^3)/3)), where r = A192918 = 0.54368901269207636157085597180174... is the real root of the equation r^2 * (1-r^3)^2 = (1-r)^2.
EXAMPLE
4.988020876600903805335224460790773050832038156091687962387444991919...
MATHEMATICA
RealDigits[E^(2*Sqrt[Log[r]^2 + 2*PolyLog[2, 1-r] - 2*PolyLog[2, 1-r^3]/3]) /. r -> (-1 - 2/(17 + 3*Sqrt[33])^(1/3) + (17 + 3*Sqrt[33])^(1/3))/3, 10, 120][[1]]
CROSSREFS
Sequence in context: A081382 A188658 A248803 * A019784 A276539 A011381
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Oct 09 2024
STATUS
approved