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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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
Wikipedia, Cevian
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
Sequence in context: A282936 A220073 A272020 * A291123 A292594 A093613
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Nov 10 2015
STATUS
approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)