OFFSET
1,4
COMMENTS
A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
A nontrivial cevian is one that does not coincide with a side of the triangle.
If a(n) = 1 then the length of the unique cevian is n^2.
It seems that a(n) = 1 if and only if n is the average of twin prime pairs divided by 2 (A040040).
LINKS
EXAMPLE
a(4) = 2 because for legs of length 4 there are two cevians, of length 6 and 16, that divide the base into two integral parts.
PROG
(PARI)
ceviso(n) = {
my(d, L=List());
for(k=1, n^2,
if(issquare(n^2+k^2-k, &d) && d!=n,
listput(L, d)
)
);
Vec(L)
}
vector(100, n, #ceviso(n))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Nov 10 2015
STATUS
approved