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 A086775 #10 Apr 19 2014 02:48:55 %S A086775 4,7,7,2,5,9,9,9,6,4,7,4,0,1,9,6,4,4,5,4,2,2,2,9,8,8,4,5,0,0,6,4,4,4, %T A086775 6,5,4,4,6,1,0,2,3,4,7,7,6,8,0,7,4,0,3,2,2,6,9,3,2,6,9,2,3,9,4,9,2,7, %U A086775 7,3,8,7,9,4,5,0,7,6,1,6,4,0,4,4,9,7,6,4,1,0,1,1,8,0,8,0,2,1,5,7,2,7,6,8,7 %N A086775 Decimal expansion of the number defined by the continued fraction shown below. %C A086775 This number is the inverse of the number whose decimal expansion is A136319. It is also the latter number minus phi. - _Geoffrey Caveney_, Apr 18 2014 %F A086775 Repeat s = s + phi; s=1/s. The initial value of s is irrelevant. %F A086775 Equals (sqrt(5+phi)-phi)/2, where phi = A001622. - _R. J. Mathar_, Sep 15 2012 %e A086775 1 %e A086775 ------ %e A086775 phi + 1 %e A086775 .... ------ %e A086775 .... phi + 1 %e A086775 ......... ------- %e A086775 ......... phi + etc %e A086775 Equals 0.477259996... %o A086775 (PARI) ?\p 2000 ?f(n) = phi=(sqrt(5)+1)/2; s=0; for(x=1,n,s=s+phi; s=1/s); print(s) %K A086775 easy,nonn,cons %O A086775 0,1 %A A086775 _Cino Hilliard_, Aug 03 2003