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A355242
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T(w,h) is the minimum integer slope >= 1 that can be chosen as orientation of a w X h rectangle such that the upper bound for the minimum number of covered grid points A354702(w,d) can be achieved by a suitable translation of the rectangle, where T(w,h) and A354702 are triangles read by rows. T(w,h) = -1 if no integer slope satisfying this condition exists.
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3
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1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 3, 3, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1
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OFFSET
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1,6
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COMMENTS
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T(17,13) = -1 is the first occurrence of the situation that it is not possible to reach the upper limit A354702(17,13) = 215 with a rectangle whose long side has an integer slope. (17 X 13)-rectangles with integer slope cannot cover less than 216 grid points. To achieve 215 grid points requires a slope of 3/2, i.e. A355241(17,13) = 3. See the linked file for related illustrations.
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LINKS
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EXAMPLE
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The triangle begins:
\ h 1 2 3 4 5 6 7 8 9 10 11 12 13
w \ --------------------------------------
1 | 1; | | | | | | | | | | | |
2 | 1, 1; | | | | | | | | | | |
3 | 1, 1, 2; | | | | | | | | | |
4 | 1, 1, 2, 1; | | | | | | | | |
5 | 1, 1, 2, 1, 3; | | | | | | | |
6 | 1, 1, 2, 1, 3, 1; | | | | | | |
7 | 1, 1, 1, 1, 1, 1, 1; | | | | | |
8 | 1, 1, 2, 1, 3, 1, 1, 2; | | | | |
9 | 1, 1, 1, 1, 3, 1, 1, 1, 1; | | | |
10 | 1, 1, 2, 1, 3, 3, 1, 2, 1, 2; | | |
11 | 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1; | |
12 | 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1; |
13 | 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1
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CROSSREFS
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A355241 is similar, but with slopes chosen from the list 1/2, 1, 3/2, 2, ... .
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KEYWORD
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AUTHOR
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STATUS
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approved
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