A248548 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.

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

Offset: 1

Author

Andreas Boe, Oct 08 2014

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Andreas Boe, Table of n, a(n) for n = 1..2426
• Andreas Boe, Sets of Pythagorean sextuples, cross indexed with the base sequence

Formula

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.