A197726 Decimal expansion of Pi/(1 + Pi).

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

Offset: 0

Author

Clark Kimberling, Oct 17 2011

Keywords

• nonn
• cons

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

Examples

			0.7585469929947761453444306890448928641384...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 1/2; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .75, .76}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197726 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2}]

PARI

1/(1/Pi+1) \\ Charles R Greathouse IV, Sep 30 2022