A197730 Decimal expansion of 3*Pi/(4+Pi).

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

Offset

1,2

Comments

Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=2/3 and c=Pi/6; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Links

Table of n, a(n) for n=1..99.

Index entries for transcendental numbers

Example

1.3197025394653278722685641235411401513975623...

Mathematica

b = 2/3; c = Pi/6;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.131, 1.132}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197730 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

Crossrefs

Cf. A197682.

Sequence in context: A052931 A368379 A006803 * A231902 A143495 A327997

Adjacent sequences: A197727 A197728 A197729 * A197731 A197732 A197733

Keyword

nonn,cons

Author

Clark Kimberling, Oct 17 2011

Status

approved