A197031 Decimal expansion of the shortest distance from x axis through (1,sqrt(2)) to y axis.

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

Offset: 1

Author

Clark Kimberling, Oct 10 2011

Keywords

• nonn
• cons

Comments

See A197008 for a discussion and guide to related sequences.

Examples

			d=3.397346951017693441277913755501410790489483...
x-intercept=(2.2599...,0)
y-intercept=(0,2.5366...)
		

Crossrefs

Cf. A197008.

Programs

Maple

(1+2^(1/3))^(3/2) ; 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 = 1; k = Sqrt[2]; d = N[f[t]^(1/2), 100]
RealDigits[d] (* A197031 *)
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 == .001, {x, 0, 4}, {y, 0, 5}], PlotRange -> All, AspectRatio -> Automatic]