login
A331244
Triangles with integer sides i <= j <= k sorted by radius of enclosing circle, and, in case of ties, lexicographically by side lengths (smallest first). The sequence gives the shortest side i. The other sides are in A331245 and A331246.
5
1, 1, 2, 2, 1, 2, 3, 2, 3, 1, 2, 3, 4, 2, 3, 3, 1, 2, 4, 3, 4, 5, 2, 3, 3, 4, 1, 4, 2, 3, 5, 4, 5, 6, 2, 3, 3, 4, 4, 5, 4, 1, 2, 5, 3, 4, 6, 5, 6, 2, 3, 3, 4, 4, 5, 5, 4, 1, 6, 2, 5, 7, 3, 4, 6, 5, 7, 6, 7, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 1, 5, 2, 3, 7, 6, 4
OFFSET
1,3
COMMENTS
The enclosing circle differs from the circumcircle by limiting the radius to (longest side)/2 for obtuse triangles, i.e., those with i^2 + j^2 < k^2.
EXAMPLE
List of triangles begins:
n
| R^2
| | i .... (this sequence)
| | | j .. (A331245)
| | | | k (A331246)
| | | | |
1 1/ 3 1 1 1
2 16/15 1 2 2
3 4/ 3 2 2 2
4 9/ 4 2 2 3 obtuse
5 81/35 1 3 3
6 81/32 2 3 3
7 3/ 1 3 3 3
8 4/ 1 2 3 4 obtuse
9 81/20 3 3 4
10 256/63 1 4 4
11 64/15 2 4 4
12 256/55 3 4 4
13 16/ 3 4 4 4
14 25/ 4 2 4 5 obtuse
15 25/ 4 3 3 5 obtuse
16 25/ 4 3 4 5
17 625/99 1 5 5
CROSSREFS
Cf. A331245 (middle side), A331246 (longest side).
Sequence in context: A216338 A227725 A365836 * A316845 A120481 A369067
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jan 20 2020
STATUS
approved