A196824 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=-c+cos(x), where c is given by A196774.

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Example

slope=-0.6341649706958779561027498118640238055822484...

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. A196823.

Sequence in context: A227989 A189088 A195301 * A309988 A275835 A257235

Adjacent sequences: A196821 A196822 A196823 * A196825 A196826 A196827

Keyword

nonn,cons

Author

Clark Kimberling, Oct 06 2011

Status

approved