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
Examples
8.46018724425296480975230009888917594335470635951014367622821158904321498...
Programs
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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]]
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)).