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 A091667 #26 Feb 16 2025 08:32:52
%S A091667 9,9,8,1,3,6,0,4,4,5,9,8,5,0,9,3,3,2,1,5,0,0,2,4,4,5,9,0,4,7,0,7,4,7,
%T A091667 3,5,3,1,1,3,8,2,9,9,4,7,6,3,0,4,3,9,8,2,1,8,5,5,8,3,8,7,4,0,7,0,3,5,
%U A091667 0,3,2,4,6,8,9,4,6,4,4,1,3,3,5,7,7,1,7,7,2,7,0,8,6,7,5,0,5,8,2,6,1,7,9,4,8
%N A091667 Decimal expansion of ((-1-sqrt(5))/2 + sqrt((5+sqrt(5))/2))*e^((2*Pi)/5).
%C A091667 Has a nice (non-simple) continued fraction due to Ramanujan.
%C A091667 Continued fraction is 1/(1+q/(1+q^2/(1+q^3/(1+...)))) where q=exp(-2*Pi). - _Michael Somos_, Sep 12 2005
%D A091667 K. Srinivas Rao, Ramanujan, a Mathematical Genius, Eastwest Books, Chennai Madras, 2000, p. 42.
%D A091667 Bruce C. Berndt and Robert A. Rankin, Ramanujan: Letters And Commentary, AMS, Providence RI, 1995, p. 29.
%D A091667 Bruce C. Berndt and Robert A. Rankin, Ramanujan: Essays And Surveys, AMS, Providence RI, 2001, p. 243.
%D A091667 G. H. Hardy, Ramanujan: Twelve Lectures on subjects as suggested by his Life and Work, AMS, Chelsea Providence RI, 1999, p. 8, section 1.11.
%H A091667 Horst Gierhardts, <a href="http://www.gierhardt.de/mathematik/ramaformeln.html">Three Famous Formulas Of Ramanujan</a>.
%H A091667 Srinivasa Ramanujan, Journal of the Indian Mathematical Society, <a href="http://www.imsc.res.in/~rao/ramanujan/collectedpapers/question/q352.htm">Question 352 (iv, 40)</a>.
%H A091667 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanContinuedFractions.html">Ramanujan Continued Fractions</a>.
%H A091667 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ramanujan%27s_continued_fractions">Ramanujan's continued fractions</a>.
%F A091667 Equals 1/A091899.
%F A091667 Equals exp(2*Pi/5) * A158934. - _Amiram Eldar_, Jan 23 2022
%e A091667 0.998136044...
%t A091667 RealDigits[Exp[2*Pi/5]*(Sqrt[(Sqrt[5] + 5)/2] - GoldenRatio), 10, 100][[1]] (* _Amiram Eldar_, Jan 23 2022 *)
%o A091667 (PARI) {a(n)=x=exp(2/5*Pi)*(sqrt((5+sqrt(5))/2)-(1+sqrt(5))/2); floor(x*10^(n+1))%10} /* _Michael Somos_, Sep 12 2005 */
%o A091667 (PARI) {a(n)= x=exp(-2*Pi); x=contfracpnqn(matrix(2,oo,i,j,if(j==1,i==1,if(i==1,x,1)^(j-2)))); x=t[1,1]/t[2,1]; floor(x*10^(n+1))%10} /* _Michael Somos_, Sep 12 2005 */
%Y A091667 Cf. A019694, A091899, A158934.
%K A091667 nonn,cons
%O A091667 0,1
%A A091667 _Eric W. Weisstein_, Jan 27 2004