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%I #5 Mar 30 2012 18:57:52
%S 5,0,6,0,9,5,4,6,4,3,7,5,4,8,9,2,5,1,4,6,3,0,1,2,3,8,5,0,4,5,3,0,6,4,
%T 4,0,9,0,0,3,3,8,5,3,3,1,4,6,5,4,0,1,5,6,1,9,5,4,2,7,4,3,1,2,0,2,7,4,
%U 0,1,6,0,2,7,6,2,4,5,2,8,2,5,8,5,5,3,7,3,3,6,6,2,2,9,6,3,7,8,4,4
%N Decimal expansion of the shortest distance from x axis through (1,e) to y axis.
%C See A197008 for a discussion and guide to related sequences.
%e d=5.06095464375489251463012385045306440900...
%e x-intercept=(2.9477...,0)
%e y-intercept=(0,4.1138...)
%t f[x_] := x^2 + (k*x/(x - h))^2; t = h + (h*k^2)^(1/3);
%t h = 1; k = E; d = N[f[t]^(1/2), 100]
%t RealDigits[d] (* A197030 *)
%t x = N[t] (* x-intercept (h,k) *)
%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, 5}], PlotRange -> All, AspectRatio -> Automatic]
%Y Cf. A197008.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 10 2011
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