cp's OEIS Frontend

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.

A200094 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 2*sin(x).

This page as a plain text file.
%I A200094 #12 Feb 12 2025 09:53:25
%S A200094 1,4,9,2,6,6,5,9,2,3,5,2,5,1,3,2,2,0,6,9,6,9,2,4,3,0,5,9,8,3,4,9,3,6,
%T A200094 8,6,1,2,4,0,4,8,8,9,5,6,1,6,3,5,6,4,3,2,6,8,3,4,4,8,4,7,9,6,0,6,9,1,
%U A200094 2,4,2,5,9,1,7,2,9,7,0,3,5,3,3,6,8,4,1,3,1,4,1,0,3,0,8,7,9,1,2
%N A200094 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 2*sin(x).
%C A200094 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200094 G. C. Greubel, <a href="/A200094/b200094.txt">Table of n, a(n) for n = 1..10000</a>
%H A200094 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200094 least x:  -0.8029921542978842507203354534748712742...
%e A200094 greatest x: 1.492665923525132206969243059834936861...
%t A200094 a = 1; b = -3; c = 2;
%t A200094 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200094 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200094 r = x /. FindRoot[f[x] == g[x], {x, -.81, -.80}, WorkingPrecision -> 110]
%t A200094 RealDigits[r]  (* A200093 *)
%t A200094 r = x /. FindRoot[f[x] == g[x], {x, 1.49, 1.50}, WorkingPrecision -> 110]
%t A200094 RealDigits[r]  (* A200094 *)
%o A200094 (PARI) a=1; b=-3; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200094 Cf. A199949.
%K A200094 nonn,cons
%O A200094 1,2
%A A200094 _Clark Kimberling_, Nov 13 2011