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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..87.

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. A128006, A128007, A192493, A192494, A331227, A331228, A331251, A331252, A331253, A331254, A331255, A331256.

Cf. A331245 (middle side), A331246 (longest side).

Sequence in context: A160735 A216338 A227725 * A316845 A120481 A219644

Adjacent sequences:  A331241 A331242 A331243 * A331245 A331246 A331247

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jan 20 2020

STATUS

approved

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Last modified February 26 18:29 EST 2020. Contains 332293 sequences. (Running on oeis4.)