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.
%I A346713 #24 Sep 01 2021 12:26:36 %S A346713 8,3,2,5,5,4,6,1,1,1,5,7,6,9,7,7,5,6,3,5,3,1,6,4,6,4,4,8,9,5,2,0,1,0, %T A346713 4,7,6,3,0,5,8,8,8,5,2,2,6,4,4,4,0,7,2,9,1,6,6,8,2,9,1,1,7,2,3,4,0,7, %U A346713 9,4,3,5,1,9,7,3,0,4,6,3,7,1,4,8,9,9,8,0 %N A346713 Decimal expansion of sqrt(log 2). %C A346713 Represents a transcendental number. %D A346713 Ludwig Seidel, Ueber eine Darstellung des Kreisbogens, des Logarithmus und des elliptischen Integrales erster Art durch unendliche Producte, Borchardt J., (1871), vol. 73, pp. 273-291. %H A346713 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A346713 Equals Product_{k>=1} (2/(2^(1/2^k) + 1))^(1/2). %F A346713 Equals sqrt(2*arccoth(3)) = sqrt(A002162). %e A346713 0.8325546111576977563531646448952010476305888522644407291668291172340794351973... %p A346713 Digits := 120; sqrt(log(2)): evalf(%)*10^91: %p A346713 ListTools:-Reverse(convert(floor(%), base, 10)); %t A346713 RealDigits[Sqrt[Log[2]], 10, 100][[1]] (* _Amiram Eldar_, Sep 01 2021 *) %o A346713 (Julia) %o A346713 using Nemo %o A346713 R = RealField(305); _1 = R(1); _2 = R(2); H = R(1/2) %o A346713 p = prod((_2/(_2^(_1/_2^k) + 1))^H for k in 1:300) %o A346713 println(p) %Y A346713 Cf. A002162. %K A346713 nonn,cons %O A346713 0,1 %A A346713 _Peter Luschny_, Sep 01 2021