A198417 - OEIS

%I #8 Feb 07 2025 16:44:05

%S 7,9,5,5,8,9,8,7,3,4,7,3,9,2,5,1,8,1,8,0,6,2,7,3,2,5,9,0,1,3,0,3,5,9,

%T 6,1,1,2,8,1,7,1,0,6,4,5,4,6,1,3,4,7,0,5,2,9,8,3,1,3,2,8,0,2,2,5,6,5,

%U 7,5,1,8,1,3,4,1,9,2,8,4,2,3,3,9,2,4,8,3,5,1,6,8,9,4,0,1,5,8,8

%N Decimal expansion of x>0 having x^2+x=2*sin(x).

%C See A198414 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 0.795589873473925181806273259013035961...

%t a = 1; b = 1; c = 2;

%t f[x_] := a*x^2 + b*x; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -1, 1}]

%t r = x /. FindRoot[f[x] == g[x], {x, .79, .80}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198417 *)

%o (PARI) solve(x=.7,1, x^2+x-2*sin(x)) \\ _Charles R Greathouse IV_, Jan 28 2025

%Y Cf. A198414.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Oct 24 2011