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A331244
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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.
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5
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..87.
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner, Jan 20 2020
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STATUS
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approved
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