cp's OEIS Frontend

A197013 Decimal expansion of the shortest distance from x axis through (1,4) to y axis.

%I A197013 #5 Mar 30 2012 18:57:52
%S A197013 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 A197013 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 A197013 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 A197013 Decimal expansion of the shortest distance from x axis through (1,4) to y axis.
%C A197013 See A197008 for a discussion and guide to related sequences.
%e A197013 d=6.60366102423402958588694523729286548481762327...
%e A197013 x-intercept=(3.5198...,0)
%e A197013 y-intercept=(0,5.5874...)
%t A197013 f[x_] := x^2 + (k*x/(x - h))^2; t = h + (h*k^2)^(1/3);
%t A197013 h = 1; k = 4; d = N[f[t]^(1/2), 100]
%t A197013 RealDigits[d] (* A197013 *)
%t A197013 x = N[t] (* x-intercept *)
%t A197013 y = N[k*t/(t - h)] (* y-intercept *)
%t A197013 Show[Plot[k + k (x - h)/(h - t), {x, 0, t}],
%t A197013  ContourPlot[(x - h)^2 + (y - k)^2 == .003, {x, 0, 4}, {y, 0, 5}], PlotRange -> All, AspectRatio -> Automatic]
%Y A197013 Cf. A197008.
%K A197013 nonn,cons
%O A197013 1,1
%A A197013 _Clark Kimberling_, Oct 10 2011