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.

A199615 Decimal expansion of least x satisfying x^2 + 4*x*cos(x) = 2*sin(x).

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%I A199615 #10 Feb 08 2025 10:14:08
%S A199615 8,5,6,3,7,4,0,4,9,7,4,4,3,4,6,1,0,9,3,2,2,0,7,8,0,6,2,5,6,4,7,2,9,1,
%T A199615 9,9,4,7,6,6,0,0,5,0,8,8,7,5,4,8,2,4,0,9,4,3,3,1,0,1,4,8,8,7,0,6,8,7,
%U A199615 1,6,7,3,4,6,5,9,9,3,0,2,8,3,6,5,7,7,2,0,9,8,7,5,0,6,7,2,7,4,5
%N A199615 Decimal expansion of least x satisfying x^2 + 4*x*cos(x) = 2*sin(x).
%C A199615 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199615 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199615 least: -0.856374049744346109322078062564729199476600...
%e A199615 greatest:  3.515613199687358023842180210704030792217...
%t A199615 a = 1; b = 4; c = 2;
%t A199615 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199615 Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t A199615 r = x /. FindRoot[f[x] == g[x], {x, -.86, -.85}, WorkingPrecision -> 110]
%t A199615 RealDigits[r]  (* A199615, least of 4 roots *)
%t A199615 r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
%t A199615 RealDigits[r]  (* A199616, greatest of 4 roots *)
%Y A199615 Cf. A199597.
%K A199615 nonn,cons
%O A199615 0,1
%A A199615 _Clark Kimberling_, Nov 08 2011
%E A199615 a(96) onwards corrected by _Georg Fischer_, Aug 03 2021