A198130 - OEIS

%I #10 Apr 14 2026 10:00:11

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

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

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

%N Decimal expansion of least x having 2*x^2+3*x=2*cos(x), negated.

%C See A197737 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 least x: -1.52799971203684063352083669388890466...

%e greatest x: 0.458061086830838048904156490023125...

%p Digits:=120:

%p fsolve(2*x^2-3*x-2*cos(x),x=1.5);  # _Alois P. Heinz_, Apr 14 2026

%t a = 2; b = 3; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -2, 1}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.53, -1.52}, WorkingPrecision -> 110]

%t RealDigits[r1](* A198130 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .45, .46}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198131 *)

%o (PARI) solve(x=-2,-1, 2*x^2+3*x-2*cos(x)) \\ _Charles R Greathouse IV_, Apr 14 2026

%Y Cf. A197737.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 22 2011

%E Name corrected by _Charles R Greathouse IV_, Apr 14 2026