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Decimal expansion of the shortest distance from x axis through (1,4) to y axis.
2

%I #5 Mar 30 2012 18:57:52

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

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

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

%N Decimal expansion of the shortest distance from x axis through (1,4) to y axis.

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

%e d=6.60366102423402958588694523729286548481762327...

%e x-intercept=(3.5198...,0)

%e y-intercept=(0,5.5874...)

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

%t h = 1; k = 4; d = N[f[t]^(1/2), 100]

%t RealDigits[d] (* A197013 *)

%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 == .003, {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