A196505 Decimal expansion of greatest x>0 satisfying sin(1/x)=1/sqrt(1+x^2).

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

Offset: 0

Author

Clark Kimberling, Oct 03 2011

Keywords

• nonn
• cons

Comments

Let M be the greatest x>0 satisfying sin(1/x)=1/sqrt(1+x^2). Then sin(1/x) > 1/sqrt(1+x^2) for all x>M=0.4929... See A196500-A196504 for related constants and inequalities.

Examples

			x=0.4929124517549075741877801898222329769156970132...
		

Crossrefs

Cf. A196500, A196502, A196503.

Programs

Mathematica

Plot[{Sin[x], x/Sqrt[1 + x^2]}, {x, 0, 9}]
Plot[{Sin[1/x], 1/Sqrt[1 + x^2]}, {x, 0.1, 1.0}] (for A196505)
t = x /.FindRoot[Sin[x] == x/Sqrt[1 + x^2], {x, .10, 3}, WorkingPrecision -> 100]
RealDigits[t]   (* A196504 *)
1/t
RealDigits[1/t] (* A196505 *)