A196823 Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=-c+cos(x), and 0<x<2*Pi.

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

Offset

0,2

Links

Table of n, a(n) for n=0..99.

Eric Weisstein's World of Mathematics, Witch of Agnesi

Example

c=0.09379002244358814064689162720210998670901288078533287...

Mathematica

Plot[{1/(1 + x^2), -.094 + Cos[x]}, {x, 0, 1}]
t = x /. FindRoot[2 x == ((1 + x^2)^2) Sin[x], {x, .5, 1}, WorkingPrecision -> 100]
RealDigits[t]     (* A196822 *)
c = N[-Cos[t] + 1/(1 + t^2), 100]
RealDigits[-c]     (* A196823 *)
slope = N[-Sin[t], 100]
RealDigits[slope] (* A196824 *)

Crossrefs

Cf. A196822.

Sequence in context: A348302 A197836 A011282 * A021520 A248313 A010539

Adjacent sequences: A196820 A196821 A196822 * A196824 A196825 A196826

Keyword

nonn,cons

Author

Clark Kimberling, Oct 06 2011

Extensions

0 prepended to get correct constant value by Michel Marcus, Feb 10 2015

Status

approved