A197724 Decimal expansion of Pi^2/(2 + Pi).

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

Offset

1,2

Comments

Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1/2 and c=1/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=1..99.

Index entries for transcendental numbers

Example

1.91956171288647865970145260737156516072232...

Mathematica

b = 1/2; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.9, 1.92}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197724 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2.8}]
RealDigits[Pi^2/(2+Pi), 10, 120][[1]] (* Harvey P. Dale, Mar 19 2023 *)

Crossrefs

Cf. A197682.

Sequence in context: A021525 A371935 A297013 * A176518 A154697 A187368

Adjacent sequences: A197721 A197722 A197723 * A197725 A197726 A197727

Keyword

nonn,cons

Author

Clark Kimberling, Oct 17 2011

Status

approved