A197685 Decimal expansion of Pi^2/(4 + 2*Pi).

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

Offset

0,1

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.

Links

Table of n, a(n) for n=0..98.

Index entries for transcendental numbers

Example

x=0.9597808564432393298507263036857825803611620667...

Mathematica

b = 1; c = 2/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .9, 1}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197685 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

Crossrefs

Cf. A197682.

Sequence in context: A341438 A265290 A293079 * A378864 A220510 A078086

Adjacent sequences: A197682 A197683 A197684 * A197686 A197687 A197688

Keyword

nonn,cons

Author

Clark Kimberling, Oct 17 2011

Status

approved