A196772 Decimal expansion of the number c for which the curve y=1/x is tangent to the curve y=sin(x-c), and 0 < x < 2*Pi; c = Pi - sqrt(r) - arccos(r-1), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset

0,1

Links

Table of n, a(n) for n=0..99.

Example

c=0.965016109773342910082904125880052671050...

Mathematica

Plot[{Sin[x + .97], 1/x}, {x, 0, Pi}]
r = GoldenRatio; x = Sqrt[r];
c = N[Pi - x - ArcCos[r - 1], 100]
RealDigits[c]      (* A196772 *)
slope = N[-1/x^2, 100]
RealDigits[slope]  (* 1-r *)

Crossrefs

Cf. A195625, A196767.

Sequence in context: A021916 A154183 A200138 * A225406 A347330 A343947

Adjacent sequences: A196769 A196770 A196771 * A196773 A196774 A196775

Keyword

nonn,cons

Author

Clark Kimberling, Oct 06 2011

Status

approved