A197014 - OEIS

%I #7 Nov 08 2022 12:47:12

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

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

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

%N Decimal expansion of the shortest distance from x axis through (2,3) to y axis.

%C See A197008 for a discussion and guide to related sequences.

%e d=7.02348237921996592684456014412915048027327616603

%e x-intercept=(4.6207...,0)

%e y-intercept=(0,5.2894...)

%p (18^(2/3)/9+1)*sqrt(18^(2/3)+9) ; evalf(%) ; # _R. J. Mathar_, Nov 08 2022

%t f[x_] := x^2 + (k*x/(x - h))^2; t = h + (h*k^2)^(1/3);

%t h = 2; k = 3; d = N[f[t]^(1/2), 100]

%t RealDigits[d] (* A197014 *)

%t x = N[t] (* x-intercept *)

%t y = N[k*t/(t - h)] (* y-intercept *)

%t Show[Plot[k + k (x - h)/(h - t), {x, 0, t}],

%t ContourPlot[(x - h)^2 + (y - k)^2 == .004, {x, 0, 4}, {y, 0, 5}], PlotRange -> All, AspectRatio -> Automatic]

%Y Cf. A197008.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 10 2011