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 A318740 #14 Aug 03 2024 13:07:46 %S A318740 1,0,4,5,0,7,7,7,1,6,1,5,8,1,3,1,5,0,8,2,4,3,0,0,4,4,2,7,8,1,6,4,0,6, %T A318740 6,0,5,2,3,1,2,8,9,4,6,5,6,0,8,3,7,9,9,3,1,5,1,8,0,2,9,6,1,8,0,0,6,5, %U A318740 2,5,2,3,7,2,2,8,3,3,8,0,4,2,3,2,1,2,2,2,3,2 %N A318740 Decimal expansion of (sqrt((5 - sqrt(5))/2) - (sqrt(5) - 1)/2) * exp(Pi/5). %C A318740 The second part of Ramanujan's question 352 in the Journal of the Indian Mathematical Society (IV, 40) asked "Show that 1 / (1 - exp(-Pi) / (1 + exp(-2*Pi) / (1 - exp(-3*Pi) / (1 + ...)))) = (sqrt((5 - sqrt(5))/2) - (sqrt(5) - 1)/2) * exp(Pi/5)". Also stated in Ramanujan's first letter to G. H. Hardy in 1913. Corrected version from page 28 of Berndt, Choi and Kang, see links. %H A318740 B. C. Berndt, Y. S. Choi, S. Y. Kang, <a href="https://faculty.math.illinois.edu/~berndt/jims.ps">The problems submitted by Ramanujan to the Journal of Indian Math. Soc.</a>, in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q352, JIMS IV). %H A318740 B. C. Berndt, Y. S. Choi, S. Y. Kang, <a href="http://citeseerx.ist.psu.edu/pdf/ae75da0be9fb455e2c55daa5fca46ae63e6a60bd">The problems submitted by Ramanujan to the Journal of Indian Math. Soc.</a>, in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q352, JIMS IV). %e A318740 1.045077716158131508243004427816406605231289465608379931518029618... %t A318740 First[RealDigits[(Sqrt[(5 - Sqrt[5])/2] - GoldenRatio + 1)*Exp[Pi/5], 10, 100]] (* _Paolo Xausa_, Apr 27 2024 *) %o A318740 (PARI) (sqrt((1/2)*(5-sqrt(5)))-(sqrt(5)-1)/2)*exp(Pi/5) %Y A318740 Cf. A091667 (part 1 of question 352). %K A318740 nonn,cons %O A318740 1,3 %A A318740 _Hugo Pfoertner_, Sep 16 2018