A196617 Decimal expansion of the least x>0 satisfying 1 = (x^2)*sin(x).

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

Offset: 1

Author

Clark Kimberling, Oct 05 2011

Keywords

• nonn
• cons

Comments

This number is the least x>0 for which there exists a constant c such that the graph of y=cos(x) is tangent to the graph of the hyperbola y=(1/x)-c, as indicated by the graph in the Mathematica program.

Examples

			1.0682235441972490182834711142630928984689...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A196619, 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; solve(x=1, 1.5, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Extensions

Terms a(88) onward corrected by G. C. Greubel, Aug 22 2018