A376659 - OEIS

%I #9 Oct 06 2024 08:48:36

%S 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,

%T 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,

%U 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

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

%F 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.

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

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

%e 3.33526020703708086029122448156335246730884987099277968...

%t 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]]

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

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Oct 01 2024