A196769 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/4).

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

Offset: 1

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Examples

			x=1.5095068322244728855653262204377685055328808170667196...
		

Crossrefs

Cf. A196772.

Programs

Mathematica

Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]     (* A196767 *)
t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196768 *)
t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196769 *)
t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196770 *)
t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196771 *)