cp's OEIS Frontend

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).

%I A196772 #8 Apr 10 2021 02:05:03
%S A196772 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,
%T A196772 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,
%U A196772 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
%N 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).
%e A196772 c=0.965016109773342910082904125880052671050...
%t A196772 Plot[{Sin[x + .97], 1/x}, {x, 0, Pi}]
%t A196772 r = GoldenRatio; x = Sqrt[r];
%t A196772 c = N[Pi - x - ArcCos[r - 1], 100]
%t A196772 RealDigits[c]      (* A196772 *)
%t A196772 slope = N[-1/x^2, 100]
%t A196772 RealDigits[slope]  (* 1-r *)
%Y A196772 Cf. A195625, A196767.
%K A196772 nonn,cons
%O A196772 0,1
%A A196772 _Clark Kimberling_, Oct 06 2011