A197691 Decimal expansion of Pi/(4 + 4*Pi).

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

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

Examples

			0.1896367482486940363361076722612232160346065914...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 2; c = 2 Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .1, .2}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197691 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[Pi/(4+4Pi),10,120][[1]] (* Harvey P. Dale, Mar 19 2025 *)