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.

A199959 Decimal expansion of least x satisfying x^2 + 3*cos(x) = 3*sin(x).

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%I A199959 #13 Feb 08 2025 23:06:12
%S A199959 1,0,4,6,4,7,2,5,4,2,5,4,0,0,9,3,4,0,3,6,1,8,0,7,3,5,5,3,7,8,6,4,3,7,
%T A199959 0,9,3,4,0,0,2,5,5,1,4,3,3,5,3,1,8,0,5,3,7,0,1,6,8,6,3,4,0,1,8,9,4,1,
%U A199959 2,2,9,6,3,9,8,0,8,4,0,8,9,4,2,8,1,2,0,4,0,6,9,5,1,7,7,0,1,9,2
%N A199959 Decimal expansion of least x satisfying x^2 + 3*cos(x) = 3*sin(x).
%C A199959 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199959 G. C. Greubel, <a href="/A199959/b199959.txt">Table of n, a(n) for n = 1..10000</a>
%H A199959 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199959 least x:  1.046472542540093403618073553786437093400...
%e A199959 greatest x: 1.9905034616684938355818760222044124763...
%t A199959 a = 1; b = 3; c = 3;
%t A199959 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199959 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199959 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A199959 RealDigits[r]   (* A199959 *)
%t A199959 r = x /. FindRoot[f[x] == g[x], {x, 1.99, 2.0}, WorkingPrecision -> 110]
%t A199959 RealDigits[r]   (* A199960 *)
%o A199959 (PARI) a=1; b=3; c=3; solve(x=1, 1.5, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A199959 Cf. A199949.
%K A199959 nonn,cons
%O A199959 1,3
%A A199959 _Clark Kimberling_, Nov 12 2011