Search: a316846 -id:a316846
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A316842
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Three-column table read by rows giving primitive integer sides of proper triangles (i,j,k) with i >= j >= k >= 1, j+k > i, gcd(i,j,k) = 1.
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+10
11
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1, 1, 1, 2, 2, 1, 3, 2, 2, 3, 3, 1, 3, 3, 2, 4, 3, 2, 4, 3, 3, 4, 4, 1, 4, 4, 3, 5, 3, 3, 5, 4, 2, 5, 4, 3, 5, 4, 4, 5, 5, 1, 5, 5, 2, 5, 5, 3, 5, 5, 4, 6, 4, 3, 6, 5, 2, 6, 5, 3, 6, 5, 4, 6, 5, 5, 6, 6, 1, 6, 6, 5, 7, 4, 4, 7, 5, 3, 7, 5, 4, 7, 5, 5, 7, 6, 2, 7, 6, 3, 7, 6, 4, 7, 6, 5, 7, 6, 6, 7, 7, 1, 7, 7, 2, 7, 7, 3, 7, 7, 4, 7, 7, 5, 7, 7, 6, 8, 5, 4
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OFFSET
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1,4
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LINKS
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EXAMPLE
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Table begins:
[1,1,1],
[2,2,1],
[3,2,2],
[3,3,1],
[3,3,2],
[4,3,2],
[4,3,3],
[4,4,1],
[4,4,3],
[5,3,3],
[5,4,2],
...
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CROSSREFS
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There are A123323(k) rows that begin with k.
See A316841 for all triples (including imprimitive triples).
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KEYWORD
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AUTHOR
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STATUS
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approved
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1, 2, 2, 3, 3, 3, 3, 4, 4, 3, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 6, 6, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9
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OFFSET
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1,2
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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1, 1, 2, 1, 2, 2, 3, 1, 3, 3, 2, 3, 4, 1, 2, 3, 4, 3, 2, 3, 4, 5, 1, 5, 4, 3, 4, 5, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 4, 5, 3, 5, 2, 3, 4, 5, 6, 7, 1, 3, 5, 7, 5, 4, 5, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 1, 2, 4, 5, 7, 8, 5, 4, 5, 6, 7, 3, 5, 7, 2, 3, 4, 5, 6
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graph;
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listen;
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OFFSET
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1,3
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A316852
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Consider primitive integer triangles as listed in rows of table A316842. Sequence gives perimeters of these triangles in the same order.
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+10
4
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3, 5, 7, 7, 8, 9, 10, 9, 11, 11, 11, 12, 13, 11, 12, 13, 14, 13, 13, 14, 15, 16, 13, 17, 15, 15, 16, 17, 15, 16, 17, 18, 19, 15, 16, 17, 18, 19, 20, 17, 18, 17, 19, 17, 18, 19, 20, 21, 22, 17, 19, 21, 23, 19, 19, 20, 19, 20, 21, 22, 23, 19, 20, 21, 22, 23, 24
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OFFSET
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1,1
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COMMENTS
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The only missing numbers are 1,2,4,6.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A317181
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Consider primitive integer triangles as listed in rows of table A316842. Sequence gives 16*area^2 for these triangles in the same order.
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+10
3
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3, 15, 63, 35, 128, 135, 320, 63, 495, 275, 231, 576, 975, 99, 384, 819, 1344, 455, 351, 896, 1575, 2304, 143, 2975, 735, 675, 1536, 2499, 495, 1280, 2295, 3456, 4655, 195, 768, 1683, 2880, 4275, 5760, 1071, 2304, 935, 3591, 663, 1728, 3135, 4800, 6615, 8448, 255, 2223, 5775, 10143
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graph;
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OFFSET
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1,1
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LINKS
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FORMULA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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