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A376841 Decimal expansion of a constant related to the asymptotics of A066447 and A333374.

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%I A376841 #3 Oct 06 2024 08:35:00
%S A376841 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,
%T A376841 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,
%U A376841 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
%N A376841 Decimal expansion of a constant related to the asymptotics of A066447 and A333374.
%F A376841 Equals limit_{n->infinity} A066447(n)^(1/sqrt(n)).
%F A376841 Equals limit_{n->infinity} A333374(n)^(1/sqrt(n)).
%F A376841 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.
%e A376841 7.1578741786143524880205016499891016064826797593549373619575862725233...
%t A376841 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]]
%Y A376841 Cf. A066447, A192918, A333374.
%K A376841 nonn,cons
%O A376841 1,1
%A A376841 _Vaclav Kotesovec_, Oct 06 2024