A197729 Decimal expansion of 3*Pi/(2 + Pi).

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

Offset: 1

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=1/3 and c=Pi/6; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			1.8330464110549718681417861638619065852122678...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 1/3; c = Pi/6;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.83, 1.84}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197729 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi}]
RealDigits[3*Pi/(2+Pi),10,120][[1]] (* Harvey P. Dale, Jun 27 2015 *)