A197683 Decimal expansion of Pi/(2+4*Pi).

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

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=1 and c=2*pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			x=0.215674359575396757213396918572837666...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 1; c = 2*Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .2, .3}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197683 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[Pi/(2+4Pi),10,120][[1]] (* Harvey P. Dale, Oct 27 2016 *)