A196609 Decimal expansion of the least x>0 satisfying 1=x*cos(4*x).

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

Offset: 1

Author

Clark Kimberling, Oct 05 2011

Keywords

• nonn
• cons

Examples

			x=1.3806085256477567291281983692950566154588360255628744...
		

Programs

Mathematica

Plot[{1/x, Cos[x], Cos[2 x], Cos[3 x], Cos[4 x]}, {x, 0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[1/x == Cos[2 x], {x, 2, 3}, WorkingPrecision -> 100]
RealDigits[t]  (* A196608 *)
t = x /. FindRoot[1/x == Cos[3 x], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196602 *)
t = x /. FindRoot[1/x == Cos[4 x], {x, .9, 1.4}, WorkingPrecision -> 100]
RealDigits[t]  (* A196609 *)
t = x /. FindRoot[1/x == Cos[5 x], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196626 *)