A197732 Decimal expansion of 2*Pi/(1 + 2*Pi).

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

Offset: 0

Author

Clark Kimberling, Oct 17 2011

Keywords

• nonn
• cons

Comments

Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1/4 and c=Pi/2; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.86269743830158702885358767429135066479590...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 1/4; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .86, .87}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197732 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]