A196610 Decimal expansion of the number c for which the curve y = c*cos(x) is tangent to the curve y = 1/x, and 0 < x < 2*Pi.

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

Offset: 1

Author

Clark Kimberling, Oct 04 2011

Keywords

• nonn
• cons

Examples

			c=1.7822251402031333124075510326661600195134426369...
		

Crossrefs

Cf. A196603, A196611.

Programs

Mathematica

Plot[{1/x, (1.78222) Cos[x]}, {x, .7, 1}]
xt = x /. FindRoot[x == Cot[x], {x, .8, 1}, WorkingPrecision -> 100]
c = N[Csc[xt]/xt^2, 100]
RealDigits[c]      (* A196610 *)
slope = -c*Sin[xt]
RealDigits[slope]  (* A196611 *)