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 A117605 #24 Mar 30 2025 16:34:41 %S A117605 5,9,6,0,7,1,6,3,7,9,8,3,3,2,1,5,2,3,1,1,2,8,0,5,4,1,4,3,9,9,6,8,1,8, %T A117605 2,8,1,1,3,3,2,5,4,9,4,3,9,6,2,1,3,1,9,4,3,2,4,7,9,0,8,3,0,3,6,0,0,5, %U A117605 1,6,2,6,8,6,2,0,8,9,1,8,5,8,7,1,6,6,0,3,3,7,5,4,2,8,4,7,5,4,7,3 %N A117605 Decimal expansion of the real solution to equation x^3 + 3*x = 2. %C A117605 Let p(n,x) denote the n-th Maclaurin polynomial of e^x, and let p'(n,x) denote its derivative. Then p'(n+1,x) = p(n,x), so that the real zero r of p(n,x), for odd n, is also the value of x that minimizes p(n+1,x). Let y = 0.5960716... . Then for n = 3, we have r = - y - 1; see A332324 for the minimal value of p(4,x). - _Clark Kimberling_, Feb 13 2020 %F A117605 x = (1+sqrt(2))^(1/3) - 1/(1+sqrt(2))^(1/3). %F A117605 From _Gerry Martens_, Mar 23 2025: (Start) %F A117605 Equals (2/3)*hypergeom([1/3, 2/3], [3/2], -1). %F A117605 Equals 2*sinh(asinh(1)/3). (End) %e A117605 x = 0.596071637983321523112805414399681828113325... %t A117605 RealDigits[N[Solve[3*z+z^3==2,z][[1,1,2]],100]][[1]] %Y A117605 Cf. A014176, A332324. %K A117605 cons,nonn %O A117605 0,1 %A A117605 _Zak Seidov_, Apr 27 2006 %E A117605 a(99) corrected by _Sean A. Irvine_, Jul 25 2021