A394368 Shortest sides z of integer-sided triangles (x <= y <= z) having at least one integral median and such that every integral median m satisfies gcd(x, y, z, m) = 1, ordered by increasing z, then y, then x.

5, 5, 7, 6, 7, 9, 10, 7, 7, 8, 12, 11, 11, 9, 16, 11, 8, 12, 9, 10, 9, 17, 13, 12, 9, 16, 16, 9, 13, 18, 11, 15, 19, 13, 13, 15, 14, 14, 11, 16, 10, 17, 12, 10, 22, 15, 19, 20, 11, 17, 21, 17, 13, 17, 17, 20, 11, 11, 16, 23, 26, 17, 29, 13, 15, 15, 14, 11, 19, 11

Offset

1,1

Comments

The longest and middle sides are in A394366 and A394367, respectively. The corresponding median values m are in A394369.

Links

Felix Huber, Table of n, a(n) for n = 1..10098

Example

5 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.
8 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

Cf. A181924, A181928, A227895, A393193, A394100, A394101, A394102, A394366, A394367, A394369.

Sequence in context: A247649 A252655 A021646 * A231589 A133888 A244587

Adjacent sequences: A394365 A394366 A394367 * A394369 A394370 A394371

Keyword

nonn

Author

Felix Huber, Mar 24 2026

Status

approved