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 A248548 Sums of Pythagorean sextuplets 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A Pythagorean sextuplet 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. LINKS Andreas Boe, Table of n, a(n) for n = 1..2426 FORMULA sum(n) = a(n)+b(n)+c(n)+d(n)+e(n)+f(n). a^2+b^2=d^2, a^2+c^2=e^2, b^2+e^2=f^2, c^2+d^2=f^2. EXAMPLE 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. CROSSREFS Sequence in context: A254839 A231456 A190414 * A252315 A131523 A307764 Adjacent sequences:  A248545 A248546 A248547 * A248549 A248550 A248551 KEYWORD nonn AUTHOR Andreas Boe, Oct 08 2014 STATUS approved

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Last modified January 22 16:37 EST 2020. Contains 331152 sequences. (Running on oeis4.)