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 A205769 #30 Aug 20 2025 10:49:56 %S A205769 3,4,2,7,0,5,0,9,8,3,1,2,4,8,4,2,2,7,2,3,0,6,8,8,0,2,5,1,5,4,8,4,5,7, %T A205769 1,7,6,5,8,0,4,6,3,7,6,9,7,0,8,6,4,4,2,9,3,2,0,3,1,7,2,9,3,4,0,5,7,8, %U A205769 9,0,6,9,4,2,2,8,3,5,3,6,7,4,5,6,0,8,1,0,8,0,6,2,8,4,0,8,6,7,0,6,2,2,7,1,3 %N A205769 Given an equilateral triangle T, partition each side (with the same orientation) into segments exhibiting the Golden Ratio. Let t be the resulting internal equilateral triangle t. Sequence gives decimal expansion of ratio of areas T/t. %C A205769 A quadratic number with denominator 2 and minimal polynomial 4x^2 - 14x + 1. - _Charles R Greathouse IV_, Apr 21 2016 %D A205769 Alfred S. Posamentier and Ingmar Lehmann, Phi, The Glorious Golden Ratio, Prometheus Books, 2011. %H A205769 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a> %H A205769 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a> %F A205769 Equals phi^2/(1 + 1/phi^2 - 1/phi). %F A205769 Equals (phi^4)/2 = 1+3*phi/2. - _Clark Kimberling_, Oct 24 2012 %e A205769 3.427050983124842272306880251548457176580463769708644293203172934... %t A205769 x = GoldenRatio; RealDigits[x^4/(1 - x + x^2), 10, 111][[1]] %o A205769 (PARI) (1+sqrt(5))^4/32 \\ _Charles R Greathouse IV_, Dec 12 2013 %Y A205769 Cf. A001622. %K A205769 nonn,cons %O A205769 1,1 %A A205769 _Robert G. Wilson v_, Jan 31 2012