A197697 Decimal expansion of (Pi^2)/(2+6*Pi).

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

Offset: 0

Author

Clark Kimberling, Oct 17 2011

Keywords

• nonn
• cons

Comments

Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=3 and c=1/Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.4733724036248419226997007643761582658652643123...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Maple

Digits:=100: evalf(Pi^2/(2+6*Pi)); # Wesley Ivan Hurt, Nov 08 2014

Mathematica

b = 3; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .15, .17}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197697 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi}]