A376658 - OEIS

%I #16 Oct 15 2024 04:57:24

%S 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,

%T 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,

%U 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

%N Decimal expansion of a constant related to the asymptotics of A376624 and A376625.

%F 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.

%F Equals limit_{n->infinity} A376624(n)^(1/sqrt(n)).

%F Equals limit_{n->infinity} A376625(n)^(1/sqrt(n)).

%F Equals limit_{n->infinity} A377075(n)^(1/sqrt(n)).

%F Equals exp(2*sqrt(2*log(A356032)^2 + polylog(2, A356032))).

%e 8.46018724425296480975230009888917594335470635951014367622821158904321498...

%t 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]]

%Y Cf. A072223, A333198, A376621, A376624, A376625, A376659, A376660, A377075.

%Y Cf. A356032.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Oct 01 2024