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A248548
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Sums of Pythagorean sextuples in increasing order: The sums of sets of six natural numbers which correspond to the lengths of the edges of a tetrahedron whose four faces are all different Pythagorean triangles.
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1
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2491, 3616, 4385, 4450, 4783, 4982, 7232, 7473, 7974, 8770, 8900, 9566, 9964, 10848, 11784, 12455, 12503, 13155, 13350, 13565, 14086, 14141, 14349, 14464, 14778, 14946, 15948, 16389, 17394, 17437, 17540, 17800, 18080, 19132, 19453, 19928, 21696, 21925, 22250, 22419, 22821, 23568, 23915, 23922, 24079
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OFFSET
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1,1
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COMMENTS
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A Pythagorean sextuple contains four Pythagorean triples.
The sequence is sorted on increasing sum of set.
See attached a-file to see the specific values in the sets.
The first sum shared by two sets is 956670.
The first set contains the values 104, 153, 672, 185, 680, 697.
The first set to have a ratio less than 2:1 between its highest and lowest value is 1680, 1925, 2052, 2555, 2652, 3277.
The method used for finding the sets was to connect two Pythagorean triangles along one edge and then calculate the length of the remaining edge.
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LINKS
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FORMULA
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Sums a + b + c + d + e + f where a^2 + b^2 = d^2, a^2 + c^2 = e^2, b^2 + e^2 = f^2, c^2 + d^2 = f^2.
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EXAMPLE
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The first value in the sequence: 2491.
104^2 + 153^2 = 185^2, 104^2 + 672^2 = 680^2, 153^2 + 680^2 = 697^2, 672^2 + 185^2 = 697^2;
104 + 153 + 185 + 672 + 680 + 697 = 2491.
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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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