A197142 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A197142

Decimal expansion of the x-intercept of the shortest segment from the x axis through (2,1) to the line y=2x.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The shortest segment from one side of an angle T through a point P inside T is called the Philo line of P in T. For discussions and guides to related sequences, see A197032, A197008 and A195284.

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

length of Philo line: 2.7463941076100...; see A197143

endpoint on x axis: (2.69141, 0)

endpoint on line y=2x: (1.1295, 2.25901)

MATHEMATICA

f[t_] := (t - k*t/(k + m*t - m*h))^2 + (m*k*t/(k + m*t - m*h))^2;

g[t_] := D[f[t], t]; Factor[g[t]]

p[t_] := h^2 k + k^3 - h^3 m - h k^2 m - 3 h k t + 3 h^2 m t + 2 k t^2 - 3 h m t^2 + m t^3

m = 2; h = 2; k = 1; (* slope m, point (h, k) *)

t = t1 /. FindRoot[p[t1] == 0, {t1, 1, 2}, WorkingPrecision -> 100]