cp's OEIS Frontend

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

%I A197012 #12 Nov 11 2022 12:57:21
%S A197012 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 A197012 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 A197012 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 A197012 Decimal expansion of the shortest distance from x axis through (1,3) to y axis.
%C A197012 See A197008 for a discussion and guide to related sequences.
%e A197012 d=5.40559872742348382543060865269562398196...
%e A197012 x-intercept=(3.0800...,0)
%e A197012 y-intercept=(0,4.4422...)
%p A197012 (3^(1/2)+1/3^(1/6))*sqrt(3^(1/3)+3) ; evalf(%) ; # _R. J. Mathar_, Nov 08 2022
%t A197012 f[x_] := x^2 + (k*x/(x - h))^2; t = h + (h*k^2)^(1/3);
%t A197012 h = 1; k = 3; d = N[f[t]^(1/2), 100]
%t A197012 RealDigits[d] (* A197012 *)
%t A197012 x = N[t] (* x-intercept *)
%t A197012 y = N[k*t/(t - h)] (* y-intercept *)
%t A197012 Show[Plot[k + k (x - h)/(h - t), {x, 0, t}],
%t A197012 ContourPlot[(x - h)^2 + (y - k)^2 == .002, {x, 0, 4}, {y, 0, 4}],PlotRange -> All, AspectRatio -> Automatic]
%Y A197012 Cf. A197008.
%K A197012 nonn,cons
%O A197012 1,1
%A A197012 _Clark Kimberling_, Oct 10 2011
%E A197012 Typo in definition corrected by _Georg Fischer_, Nov 11 2022