cp's OEIS Frontend

A199611 Decimal expansion of least x satisfying x+4*cos(x)=0.

%I A199611 #8 Feb 07 2025 19:50:23
%S A199611 1,2,5,2,3,5,3,2,3,4,0,0,2,5,8,8,7,6,3,1,8,6,3,2,8,1,2,1,9,7,5,3,8,0,
%T A199611 4,3,5,9,0,1,2,8,0,6,1,0,5,6,6,1,8,9,9,9,2,3,8,6,1,4,4,3,1,3,0,8,0,8,
%U A199611 0,2,4,1,3,3,5,3,2,6,7,5,6,7,8,9,0,9,6,2,7,6,9,1,9,2,7,6,2,0,1
%N A199611 Decimal expansion of least x satisfying x+4*cos(x)=0.
%C A199611 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199611 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199611 least: -1.25235323400258876318632812197538043590128...
%e A199611 greatest:  3.59530486716154799187760693508341871491...
%t A199611 a = 1; b = 4; c = 0;
%t A199611 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199611 Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t A199611 r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
%t A199611 RealDigits[r]  (* A199611, least of 4 roots *)
%t A199611 r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
%t A199611 RealDigits[r]  (* A199612, greatest of 4 roots *)
%Y A199611 Cf. A199597.
%K A199611 nonn,cons
%O A199611 1,2
%A A199611 _Clark Kimberling_, Nov 08 2011