OFFSET
1,1
COMMENTS
If the medians to two distinct sides of an integer triangle were integral, then parity in 4*m^2 = 2*y^2 + 2*z^2 - x^2 would force x, y, z to be even. Under the gcd condition this would lead to infinite 2-adic descent unless the two medians coincided. Hence at most one distinct integral median length can occur (in the isosceles case two medians may exist geometrically, but they are equal).
LINKS
Felix Huber, Table of n, a(n) for n = 1..10098
EXAMPLE
4 is a term because in the triangle (x, y, z) = (5, 5, 6) the median to z = 6 has length m = 4. It splits z into 3 and 3, yielding two congruent triangles (3, 4, 5), and gcd(5, 5, 6, 4) = 1.
7 is a term because in the triangle (x, y, z) = (7, 8, 9) the median to y = 8 has length m = 7. It splits y into 4 and 4, yielding triangles (4, 7, 7) and (4, 7, 9), and gcd(7, 8, 9, 7) = 1.
9 is a term because in the triangle (x, y, z) = (8, 14, 14) the medians to y = 14 and z = 14 both have length m = 9. Each splits the side into 7 and 7, yielding triangles (7, 8, 9) and (7, 9, 14), and gcd(8, 14, 14, 9) = 1.
MAPLE
# See Huber link in A394366.
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Huber, Mar 24 2026
STATUS
approved
