A197736 Decimal expansion of 4*Pi/(1 + Pi).

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

Offset: 1

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=1/8 and c=Pi/8; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			3.03418797197910458137772275617957145655370...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 1/8; c = Pi/8;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 3, 4}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197736 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 8*Pi}]
RealDigits[(4Pi)/(1+Pi ),10,120][[1]] (* Harvey P. Dale, Feb 26 2024 *)