A196823 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

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 *)