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 A229780 #62 Feb 24 2025 06:27:09 %S A229780 5,2,3,6,0,6,7,9,7,7,4,9,9,7,8,9,6,9,6,4,0,9,1,7,3,6,6,8,7,3,1,2,7,6, %T A229780 2,3,5,4,4,0,6,1,8,3,5,9,6,1,1,5,2,5,7,2,4,2,7,0,8,9,7,2,4,5,4,1,0,5, %U A229780 2,0,9,2,5,6,3,7,8,0,4,8,9,9,4,1,4,4,1,4,4,0,8,3,7,8,7,8,2,2,7 %N A229780 Decimal expansion of (3+sqrt(5))/10. %C A229780 sqrt((3+sqrt(5))/10) = sqrt(phi^2/5) = (5+sqrt(5))/10 = (3+sqrt(5))/10 + 2/10 = 0.723606797... . %C A229780 Essentially the same as A134972, A134945, A098317 and A002163. - _R. J. Mathar_, Sep 30 2013 %C A229780 Equals one tenth of the limit of (G(n+2)+G(n+1)+G(n-1)+G(n-2))/G(n), where G(n) is any nonzero sequence satisfying the recurrence G(n+1) = G(n) + G(n-1) including A000032 and A000045, as n --> infinity. - _Richard R. Forberg_, Nov 17 2014 %C A229780 3+sqrt(5) is the perimeter of a golden rectangle with a unit width. - _Amiram Eldar_, May 18 2021 %C A229780 Constant x such that x = sqrt(x) - 1/5. - _Andrea Pinos_, Jan 15 2024 %F A229780 (3+sqrt(5))/10 = (phi/sqrt(5))^2 = phi^2/5 where phi is the golden ratio. %e A229780 0.5236067977499... %t A229780 RealDigits[GoldenRatio^2/5,10,120][[1]] (* _Harvey P. Dale_, Dec 02 2014 *) %Y A229780 Cf. A094874, A187798. %K A229780 cons,nonn,easy %O A229780 0,1 %A A229780 _Joost Gielen_, Sep 29 2013