cp's OEIS Frontend

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.

%I A331244 #5 Jan 20 2020 13:05:11
%S A331244 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,
%T A331244 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,
%U A331244 7,2,3,3,4,4,4,5,5,5,6,6,1,5,2,3,7,6,4
%N 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.
%C A331244 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.
%e A331244 List of triangles begins:
%e A331244    n
%e A331244    |     R^2
%e A331244    |     |    i .... (this sequence)
%e A331244    |     |    | j .. (A331245)
%e A331244    |     |    | | k  (A331246)
%e A331244    |     |    | | |
%e A331244    1    1/ 3  1 1 1
%e A331244    2   16/15  1 2 2
%e A331244    3    4/ 3  2 2 2
%e A331244    4    9/ 4  2 2 3  obtuse
%e A331244    5   81/35  1 3 3
%e A331244    6   81/32  2 3 3
%e A331244    7    3/ 1  3 3 3
%e A331244    8    4/ 1  2 3 4  obtuse
%e A331244    9   81/20  3 3 4
%e A331244   10  256/63  1 4 4
%e A331244   11   64/15  2 4 4
%e A331244   12  256/55  3 4 4
%e A331244   13   16/ 3  4 4 4
%e A331244   14   25/ 4  2 4 5  obtuse
%e A331244   15   25/ 4  3 3 5  obtuse
%e A331244   16   25/ 4  3 4 5
%e A331244   17  625/99  1 5 5
%Y A331244 Cf. A128006, A128007, A192493, A192494, A331227, A331228, A331251, A331252, A331253, A331254, A331255, A331256.
%Y A331244 Cf. A331245 (middle side), A331246 (longest side).
%K A331244 nonn
%O A331244 1,3
%A A331244 _Hugo Pfoertner_, Jan 20 2020