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 A094874 #45 Nov 28 2024 14:45:06
%S A094874 1,3,8,1,9,6,6,0,1,1,2,5,0,1,0,5,1,5,1,7,9,5,4,1,3,1,6,5,6,3,4,3,6,1,
%T A094874 8,8,2,2,7,9,6,9,0,8,2,0,1,9,4,2,3,7,1,3,7,8,6,4,5,5,1,3,7,7,2,9,4,7,
%U A094874 3,9,5,3,7,1,8,1,0,9,7,5,5,0,2,9,2,7,9,2,7,9,5,8,1,0,6,0,8,8,6,2,5,1,5,2,4
%N A094874 Decimal expansion of (5-sqrt(5))/2.
%C A094874 Also the limiting ratio of Lucas(n)/Fibonacci(n+1), or Fibonacci(n-1)/Fibonacci(n+1) + 1. - _Alexander Adamchuk_, Oct 10 2007
%H A094874 Ivan Panchenko, <a href="/A094874/b094874.txt">Table of n, a(n) for n = 1..1000</a>
%H A094874 Paul Cooijmans, <a href="http://web.archive.org/web/20050302174449/http://members.chello.nl/p.cooijmans/gliaweb/tests/odds.html">Odds</a>.
%H A094874 Yiyan Ni, Myron Hlynka, and Percy H. Brill, <a href="https://arxiv.org/abs/1806.09150">Urn Models and Fibonacci Series</a>, arXiv:1806.09150 [math.CO], 2018. See (9) p. 7.
%H A094874 Jonathan Sondow, <a href="https://arxiv.org/abs/1106.4246">Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers</a>, arXiv:1106.4246 [math.NT], 2011; Diophantine Analysis and Related Fields 2011 - AIP Conference Proceedings, vol. 1385, pp. 97-100.
%H A094874 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A094874 Equals (2-phi)*(2+phi) = 2 - 1/phi = 3 - phi = (5-sqrt(5))/2 = (2*sin(Pi/5))^2, where phi is the golden ratio (A001622).
%F A094874 Equals Product_{n > 0} (1 + 1/A192223(n)). - _Charles R Greathouse IV_, Jun 26 2011
%F A094874 Equals 1 + Sum_{k >= 2} (-1)^k/(Fibonacci(k)*Fibonacci(k+1)). See Ni et al. - _Michel Marcus_, Jun 26 2018; corrected by _Michel Marcus_, Mar 11 2024
%F A094874 Equals Sum_{k>=0} binomial(2*k,k)/((k+1) * 5^k). - _Amiram Eldar_, Aug 03 2020
%F A094874 From _Amiram Eldar_, Nov 28 2024: (Start)
%F A094874 Equals 5*A244847 = 2*A187798 = 1/A242671 = A182007^2 = sqrt(A187426).
%F A094874 Equals Product_{k>=1} (1 + 1/A081012(k)). (End)
%e A094874 1.38196601125010515179541316563436188...
%t A094874 RealDigits[5/2 - Sqrt[5]/2, 10, 100][[1]] (* _Alonso del Arte_, Jun 26 2018 *)
%o A094874 (PARI) (5-sqrt(5))/2 \\ _Charles R Greathouse IV_, Jun 26 2011
%Y A094874 Equals A079585-1.
%Y A094874 Cf. A000032, A000045, A081012, A182007, A187426, A187798, A192223, A242671, A244847.
%K A094874 cons,nonn,easy
%O A094874 1,2
%A A094874 _N. J. A. Sloane_, Jun 14 2004