A264263 The number of distinct nontrivial integral cevians of an isosceles triangle, with base of length 1 and legs of length n, that divide the base into two integral parts.

0, 1, 1, 2, 2, 1, 3, 3, 1, 3, 3, 2, 5, 3, 1, 3, 7, 3, 3, 3, 1, 5, 5, 2, 5, 3, 3, 7, 3, 1, 5, 11, 3, 3, 3, 1, 5, 11, 3, 4, 4, 3, 7, 3, 3, 7, 7, 3, 5, 5, 1, 7, 7, 1, 3, 3, 3, 11, 11, 5, 5, 7, 3, 3, 3, 3, 15, 7, 1, 3, 7, 7, 11, 5, 1, 5, 11, 3, 3, 7, 3, 7, 7, 2

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

Colin Barker, Table of n, a(n) for n = 1..1000

Wikipedia, Cevian

Wikipedia, Isosceles triangle

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

Cf. A040040, A264264.

Sequence in context: A282936 A220073 A272020 * A291123 A292594 A093613

Adjacent sequences: A264260 A264261 A264262 * A264264 A264265 A264266

Keyword

nonn,easy

Author

Colin Barker, Nov 10 2015

Status

approved