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A198311
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Minimum perimeter of n-tuples of Heronian triangles with equal perimeter and equal area.
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3
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12, 70, 98, 448, 1170, 2340, 11700, 84630, 94668, 428736, 662676, 1325352
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OFFSET
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1,1
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COMMENTS
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Kurz's paper reports the first 10 values in a table on page 193, but for some reason the areas are multiplied by 4 (A204559) and the last two values are incorrect since correspond to n-tuples which are not minimal.
If n-tuples were sorted by area instead, a(2) would have been 84, corresponding to triangles (10, 35, 39), (14, 30, 40) with common minimal area 168.
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LINKS
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EXAMPLE
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The first 3 entries and corresponding triangles:
a(1) = p = 12, A = 6, T = (3, 4, 5);
a(2) = p = 70, A = 210, T = (17, 25, 28), (20, 21, 29);
a(3) = p = 98, A = 420, T = (24, 37, 37), (25, 34, 39), (29, 29, 40).
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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a(9)-a(10) corrected and a(11)-a(12) added by Giovanni Resta, Apr 21 2020
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STATUS
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approved
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