A264263 -id:A264263 - cp's OEIS frontend

A264264 The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides the base into two integral parts.

4, 9, 6, 9, 36, 11, 14, 81, 16, 19, 30, 15, 24, 225, 26, 19, 48, 31, 34, 441, 36, 39, 84, 35, 44, 69, 32, 49, 900, 51, 34, 87, 56, 59, 1296, 61, 40, 141, 66, 69, 108, 49, 74, 159, 64, 53, 126, 81, 84, 2601, 86, 89, 2916, 91, 94, 147, 66, 61, 66, 101, 70, 165

Offset: 2

Colin Barker, Nov 10 2015

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.
For all n, the longest nontrivial integral cevian has length n^2.

			a(4) = 6 because for legs of length 4 there are two cevians, of length 6 and 16, that divide the base into two integral parts.

Colin Barker, Table of n, a(n) for n = 2..1000
Wikipedia, Cevian
Wikipedia, Isosceles triangle

Cf. A264263.

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, n++; ceviso(n)[1])

cp's OEIS Frontend

A264264 The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides the base into two integral parts.

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