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.

A199621 Decimal expansion of x<0 satisfying 2*x+cos(x)=0.

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%I A199621 #10 Feb 07 2025 19:51:30
%S A199621 4,5,0,1,8,3,6,1,1,2,9,4,8,7,3,5,7,3,0,3,6,5,3,8,6,9,6,7,6,2,6,8,1,8,
%T A199621 2,7,3,2,0,1,3,6,5,0,1,7,2,3,0,5,5,4,3,4,0,1,5,0,5,8,4,9,1,3,6,3,6,4,
%U A199621 1,5,6,6,9,8,5,2,2,3,3,7,9,5,4,7,4,1,4,1,3,3,0,6,9,9,2,3,1,6,2
%N A199621 Decimal expansion of x<0 satisfying 2*x+cos(x)=0.
%C A199621 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%C A199621 This is the abscissa point x = 0.45018... where a parabola y=x^2+a and the curve y=sin(x) touch at exactly one point, a=0.23246557... - _R. J. Mathar_, Aug 27 2024
%H A199621 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199621 -0.450183611294873573036538696762681827320...
%t A199621 a = 2; b = 1; c = 0;
%t A199621 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199621 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A199621 r = x /. FindRoot[f[x] == g[x], {x, -.46, -.45}, WorkingPrecision -> 110]
%t A199621 RealDigits[r]  (* A199621 *)
%Y A199621 Cf. A199597.
%K A199621 nonn,cons
%O A199621 0,1
%A A199621 _Clark Kimberling_, Nov 08 2011