A197727 Decimal expansion of 2*Pi/(2+Pi).

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

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=1/2 and c=Pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

One-half of the harmonic mean of 2 and Pi. - Wesley Ivan Hurt, Sep 02 2014

Examples

			1.22203094070331457876119077590793772347484...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Maple

Digits:=100: evalf(2*Pi/(2+Pi)); # Wesley Ivan Hurt, Sep 02 2014

Mathematica

b = 1/2; c = Pi/4;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.22, 1.23}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197727 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2}]

Formula

Continued fraction: 1 + 1/(4 + 3/(4 + 15/(4 + ... + (4*n^2 - 1)/(4 + ... )))). - Peter Bala, Feb 27 2024