A331254 - OEIS

A331254

Triangles with integer sides i <= j <= k sorted by radius of circumcircle, and, in case of ties, lexicographically by side lengths (smallest first). The sequence gives the shortest side i. The other sides are in A331255 and A331256.

%I #8 Jan 19 2020 20:40:47

%S 1,1,2,2,1,2,3,3,1,2,2,3,4,3,1,2,4,3,2,3,4,5,3,1,4,4,2,3,5,4,2,5,3,6,

%T 5,4,1,3,2,4,5,3,4,6,5,2,6,4,5,1,6,2,3,3,5,7,3,4,4,4,6,5,5,7,6,2,7,4,

%U 6,1,5,5,2,6,3,3,7,6,4,8,5,4,7,3,5,6,8

%N Triangles with integer sides i <= j <= k sorted by radius of circumcircle, and, in case of ties, lexicographically by side lengths (smallest first). The sequence gives the shortest side i. The other sides are in A331255 and A331256.

%e List of triangles begins:

%e n

%e | R^2 = A331227(n)/A331228(n)

%e | | i .... (this sequence)

%e | | | j .. (A331255)

%e | | | | k (A331256)

%e | | | | |

%e 1 1/ 3 1 1 1

%e 2 16/15 1 2 2

%e 3 4/ 3 2 2 2

%e 4 16/ 7 2 2 3

%e 5 81/35 1 3 3

%e 6 81/32 2 3 3

%e 7 3/ 1 3 3 3

%e 8 81/20 3 3 4

%e 9 256/63 1 4 4

%e 10 64/15 2 3 4

%e 11 64/15 2 4 4

%e 12 256/55 3 4 4

%Y Cf. A331227, A331228, A331251, A331252, A331253.

%Y Cf. A331255 (middle side), A331256 (longest side).

%K nonn

%O 1,3

%A _Hugo Pfoertner_, Jan 19 2020