_Clark Kimberling (ck6(AT)evansville.edu), _, Oct 24 2011

OEIS Server: https://oeis.org/edit/global/285

proposed

approved

editing

proposed

allocatedDecimal expansion of least forx Clarkhaving Kimberling4*x^2+3x=4*cos(x).

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

1,3

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

least x: -1.128864420523986139477004663061889573...

greatest x: 0.6060777836486264536657977579905629...

a = 4; b = 3; c = 4;

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

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

r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]

RealDigits[r1] (* A198367 *)

r2 = x /. FindRoot[f[x] == g[x], {x, .60, .61}, WorkingPrecision -> 110]

RealDigits[r2] (* A198368 *)

Cf. A197737.

allocated

nonn,cons

Clark Kimberling (ck6(AT)evansville.edu), Oct 24 2011

approved

editing

allocated for Clark Kimberling

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