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A246918 The length of the shortest nontrivial integral cevian of an equilateral triangle of side n that divides an edge into two integral parts, or 0 if no such cevian exists.

%I A246918 #23 Dec 10 2016 19:35:15
%S A246918 0,0,7,0,7,14,13,7,21,14,31,28,43,26,13,14,73,42,91,28,19,62,133,21,
%T A246918 35,86,63,52,211,26,241,28,37,146,31,84,343,182,49,35,421,38,463,124,
%U A246918 39,266,553,42,91,70,79,172,703,126,49,49,97,422,871,52,931,482
%N A246918 The length of the shortest nontrivial integral cevian of an equilateral triangle of side n that divides an edge into two integral parts, or 0 if no such cevian exists.
%C A246918 A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
%C A246918 A nontrivial cevian is one that does not coincide with a side of the triangle.
%C A246918 For an equilateral triangle of side n, the lengths of its cevians are the values of y in the solutions to x^2-y^2-n*x+n^2=0.
%H A246918 Colin Barker, <a href="/A246918/b246918.txt">Table of n, a(n) for n = 1..10000</a>
%H A246918 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cevian">Cevian</a>
%o A246918 (PARI)
%o A246918 \\ Returns the length of the shortest integral cevian of an equilateral triangle of side n.
%o A246918 shortest(n) = {
%o A246918   s=[];
%o A246918   m=12*n^2;
%o A246918   fordiv(m, f,
%o A246918     g=m\f;
%o A246918     if(f<=g && (f+g)%2==0,
%o A246918       x=(f+g)\2;
%o A246918       if(x%4==0,
%o A246918         s=concat(s, x\4)
%o A246918       )
%o A246918     )
%o A246918   );
%o A246918   s=Colrev(s)~;
%o A246918   if(#s==1, return(0));
%o A246918   for(i=1, #s, if(s[i]!=n, return(s[i])))
%o A246918 }
%o A246918 vector(100, n, shortest(n))
%Y A246918 Cf. A229839, A246919, A246920.
%K A246918 nonn
%O A246918 1,3
%A A246918 _Colin Barker_, Sep 07 2014