cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A333198 Decimal expansion of a constant related to the asymptotics of A306734 and A333179.

This page as a plain text file.
%I A333198 #11 Oct 07 2024 11:21:38
%S A333198 1,8,6,4,2,9,5,2,5,4,3,5,8,4,4,0,6,5,9,2,4,7,4,7,5,9,9,8,5,6,1,1,2,2,
%T A333198 4,6,8,7,7,2,9,5,2,4,4,5,0,7,3,6,8,4,2,1,5,7,4,4,0,3,3,6,0,1,5,8,1,4,
%U A333198 1,1,9,7,8,0,4,6,0,8,4,7,9,1,1,3,6,4,7,9,6,6,0,9,8,3,6,9,6,7,6,3,5,1,8,2,4
%N A333198 Decimal expansion of a constant related to the asymptotics of A306734 and A333179.
%F A333198 Equals limit_{n->infinity} A306734(n)^(1/sqrt(n)).
%F A333198 Equals limit_{n->infinity} A333179(n)^(1/sqrt(n)).
%F A333198 Equals exp(sqrt(4*log(r)^2/3 + 4*polylog(2, 1-r) - Pi^2/3)), where r = 1 - A357471 = 0.4301597090019467340886... is the real root of the equation r^2 = (1-r)^3. - _Vaclav Kotesovec_, Oct 07 2024
%e A333198 1.86429525435844065924747599856112246877295244507368421574403...
%t A333198 RealDigits[E^Sqrt[4*Log[r]^2/3 + 4*PolyLog[2, 1-r] - Pi^2/3] /. r -> (2 - 5*(2/(-11 + 3*Sqrt[69]))^(1/3) + ((-11 + 3*Sqrt[69])/2)^(1/3))/3, 10, 120][[1]] (* _Vaclav Kotesovec_, Oct 07 2024 *)
%Y A333198 Cf. A306734, A333179, A333180, A333181, A357471, A376621.
%K A333198 nonn,cons
%O A333198 1,2
%A A333198 _Vaclav Kotesovec_, Mar 11 2020
%E A333198 More digits from _Vaclav Kotesovec_, Oct 07 2024