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A199613 Decimal expansion of least x satisfying x^2+4*x*cos(x)=sin(x) (negated).

%I A199613 #13 Feb 08 2025 13:24:02
%S A199613 1,0,7,7,3,0,9,9,1,7,5,2,4,0,7,2,0,3,0,3,3,9,9,7,9,6,1,5,1,2,6,8,1,3,
%T A199613 6,6,4,7,9,1,6,5,3,9,9,5,8,3,8,5,8,7,9,3,4,0,9,3,3,1,5,0,2,2,5,4,2,0,
%U A199613 7,7,4,2,2,3,3,2,4,7,1,0,7,3,0,2,3,3,9,5,0,3,9,8,7,4,5,2,2,8,9
%N A199613 Decimal expansion of least x satisfying x^2+4*x*cos(x)=sin(x) (negated).
%C A199613 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199613 Iain Fox, <a href="/A199613/b199613.txt">Table of n, a(n) for n = 1..20000</a>
%H A199613 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199613 least: -1.077309917524072030339979615126813664791...
%e A199613 greatest: 3.553241680682892523957265556234494902067...
%t A199613 a = 1; b = 4; c = 1;
%t A199613 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199613 Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t A199613 r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
%t A199613 RealDigits[r]  (* A199613, least of 4 roots *)
%t A199613 r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
%t A199613 RealDigits[r]  (* A199614, greatest of 4 roots *)
%o A199613 (PARI) solve(x=-2, -1, x^2+4*x*cos(x)-sin(x)) \\ _Iain Fox_, Nov 22 2017
%Y A199613 Cf. A199597.
%K A199613 nonn,cons
%O A199613 1,3
%A A199613 _Clark Kimberling_, Nov 08 2011