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 A090655 #14 Feb 03 2025 12:24:06 %S A090655 9,9,0,8,3,2,6,9,1,3,1,9,5,9,8,3,9,3,9,6,7,8,8,3,1,9,0,1,2,0,5,7,4,3, %T A090655 9,1,9,3,7,6,9,4,4,8,6,0,7,6,7,8,6,9,3,1,9,0,6,5,6,7,9,5,8,4,3,4,0,7, %U A090655 5,0,4,2,2,4,3,9,5,1,5,6,6,7,8,0,6,9,2,8,6,2,3,0,2,7,7,3,6,0,7,6,5 %N A090655 Decimal expansion of solution to n/x = x-n for n = 9. %C A090655 n/x = x-n with n=1 gives the Golden Ratio = 1.6180339887... %C A090655 Equals n +n/(n +n/(n +n/(n +....))) for n = 9. See also A090388. - _Stanislav Sykora_, Jan 23 2014 %H A090655 G. C. Greubel, <a href="/A090655/b090655.txt">Table of n, a(n) for n = 1..10000</a> %H A090655 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>. %F A090655 n/x = x-n ==> x^2 - n*x - n = 0 ==> x = (n + sqrt(n^2 + 4*n)) / 2 (Positive Root) n = 9: x = (9 + sqrt(117))/2 = 9.90832691319598... %F A090655 Equals (3/2)*(3 + sqrt(13)). - _G. C. Greubel_, Jul 03 2017 %e A090655 9.90832691319598... %t A090655 RealDigits[(3/2)*(3+Sqrt[13]), 10, 50][[1]] (* _G. C. Greubel_, Jul 03 2017 *) %o A090655 (PARI) (3/2)*(3 + sqrt(13)) \\ _G. C. Greubel_, Jul 03 2017 %Y A090655 Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A090550 (n=5), A092294 (n=6), A092290 (n=7), A090654 (n=8), A090656 (n=10). - _Stanislav Sykora_, Jan 23 2014 %K A090655 easy,nonn,cons %O A090655 1,1 %A A090655 _Felix Tubiana_, Feb 05 2004