A197012 Decimal expansion of the shortest distance from x axis through (1,3) to y axis.

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

Offset

1,1

Comments

See A197008 for a discussion and guide to related sequences.

Links

Table of n, a(n) for n=1..100.

Example

d=5.40559872742348382543060865269562398196...
x-intercept=(3.0800...,0)
y-intercept=(0,4.4422...)

Maple

(3^(1/2)+1/3^(1/6))*sqrt(3^(1/3)+3) ; 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 = 3; d = N[f[t]^(1/2), 100]
RealDigits[d] (* A197012 *)
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 == .002, {x, 0, 4}, {y, 0, 4}], PlotRange -> All, AspectRatio -> Automatic]

Crossrefs

Cf. A197008.

Sequence in context: A153106 A021189 A320411 * A200137 A197384 A193035

Adjacent sequences: A197009 A197010 A197011 * A197013 A197014 A197015

Keyword

nonn,cons

Author

Clark Kimberling, Oct 10 2011

Extensions

Typo in definition corrected by Georg Fischer, Nov 11 2022

Status

approved