A196619 Decimal expansion of the number c for which the curve y=cos(x) is tangent to the curve y=(1/x)-c, and 0

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

Offset: 0

Author

Clark Kimberling, Oct 05 2011

Keywords

• nonn
• cons

Examples

			x = 0.454451866354226599819691146329523402836346961...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A196617, A196618, A196620, A196612.

Programs

Mathematica

Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
RealDigits[xt]      (* A196617 *)
Cos[xt]
RealDigits[Cos[xt]] (* A196618 *)
c = N[1/xt - Cos[xt], 100]
RealDigits[c]       (* A196619 *)
slope = -Sin[xt]
RealDigits[slope]   (* A196620 *)

PARI

a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); 1/x - cos(x) \\ G. C. Greubel, Aug 22 2018