A197014 Decimal expansion of the shortest distance from x axis through (2,3) to y axis.

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, 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, 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

Offset: 1

Author

Clark Kimberling, Oct 10 2011

Keywords

• nonn
• cons

Comments

See A197008 for a discussion and guide to related sequences.

Examples

			d=7.02348237921996592684456014412915048027327616603
x-intercept=(4.6207...,0)
y-intercept=(0,5.2894...)
		

Crossrefs

Cf. A197008.

Programs

Maple

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

Mathematica

f[x_] := x^2 + (k*x/(x - h))^2; t = h + (h*k^2)^(1/3);
h = 2; k = 3; d = N[f[t]^(1/2), 100]
RealDigits[d] (* A197014 *)
x = N[t] (* x-intercept *)
y = N[k*t/(t - h)] (* y-intercept *)
Show[Plot[k + k (x - h)/(h - t), {x, 0, t}],
ContourPlot[(x - h)^2 + (y - k)^2 == .004, {x, 0, 4}, {y, 0, 5}], PlotRange -> All, AspectRatio -> Automatic]