A197733 Decimal expansion of 2*Pi/(1+Pi).

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

Offset: 1

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=1/4 and c=Pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Equals the harmonic mean of 1 and Pi. - Stanislav Sykora, Apr 11 2016

Examples

			1.51709398598955229068886137808978572827685273...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A074950 (harmonic mean of Pi and e), A197682.

Programs

MATLAB

2*pi/(1+pi) % Altug Alkan, Apr 11 2016

Mathematica

b = 1/4; c = Pi/4;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.517, 1.518}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197733 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[2Pi/(1+Pi),10,120][[1]] (* Harvey P. Dale, Jun 17 2022 *)

PARI

2*Pi/(1+Pi) \\ Michel Marcus, Apr 11 2016