A197693 Decimal expansion of (Pi^2)/(4+4*Pi).

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

Offset

0,1

Comments

Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=2 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=0.59576141514875427327955317355865250501468575843...

Mathematica

b = 2; c = 2/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .5, .6}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197693 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[Pi^2/(4+4*Pi), 10, 120][[1]] (* Harvey P. Dale, Nov 27 2022 *)

Crossrefs

Cf. A197682.

Sequence in context: A275810 A302708 A108781 * A117014 A200283 A355178

Adjacent sequences: A197690 A197691 A197692 * A197694 A197695 A197696

Keyword

nonn,cons

Author

Clark Kimberling, Oct 17 2011

Status

approved