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Decimal expansion of the shortest distance from x axis through (1,3) to y axis.
2

%I #12 Nov 11 2022 12:57:21

%S 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,

%T 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,

%U 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

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

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

%e d=5.40559872742348382543060865269562398196...

%e x-intercept=(3.0800...,0)

%e y-intercept=(0,4.4422...)

%p (3^(1/2)+1/3^(1/6))*sqrt(3^(1/3)+3) ; 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 = 1; k = 3; d = N[f[t]^(1/2), 100]

%t RealDigits[d] (* A197012 *)

%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 == .002, {x, 0, 4}, {y, 0, 4}],PlotRange -> All, AspectRatio -> Automatic]

%Y Cf. A197008.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 10 2011

%E Typo in definition corrected by _Georg Fischer_, Nov 11 2022