A197684 Decimal expansion of Pi^2/(2 + 2*Pi).

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

Offset

1,3

Comments

Least x > 0 such that sin(bx) = cos(cx) (and also sin(cx) = cos(bx)), where b=1 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

1.191522830297508546559106347117305010029371...

Mathematica

b = 1; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.1, 1.2}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197684 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

Crossrefs

Cf. A197682.

Sequence in context: A327963 A328112 A328097 * A121224 A100924 A350885

Adjacent sequences: A197681 A197682 A197683 * A197685 A197686 A197687

Keyword

nonn,cons

Author

Clark Kimberling, Oct 17 2011

Extensions

Offset changed by Georg Fischer, Jul 29 2021

Status

approved