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A268396
Sides of Pythagorean cuboids: triples (a, b, c) that are integral length sides of a rectangular cuboid for which the three face diagonals x, y, z also have integral length.
2
44, 117, 240, 240, 252, 275, 88, 234, 480, 85, 132, 720, 160, 231, 792, 132, 351, 720, 140, 480, 693, 480, 504, 550, 176, 468, 960, 170, 264, 1440, 220, 585, 1200, 720, 756, 825, 320, 462, 1584, 264, 702, 1440, 280, 960, 1386, 187, 1020, 1584, 308, 819, 1680
OFFSET
1,1
COMMENTS
Sides in increasing order of perimeter (a+b+c), where a < b < c.
A triple (a, b, c) of integers belongs to this sequence if and only if all of the numbers sqrt(a^2 + b^2), sqrt(b^2 + c^2), and sqrt(a^2 + c^2) are also integers.
Consider the set S(n) = {a(3*n-2), a(3*n-1), a(3*n)}. Then:
- at least one number in the set is divisible by 5
- at least one number in the set is divisible by 9
- at least one number in the set is divisible by 11
- at least one number in the set is divisible by 16
- at least two numbers in the set are divisible by 3
- at least two numbers in the set are divisible by 4.
The list of "Sides of ..." is A195816, while this sequence lists "Triples...", i.e., (a(3n-2), a(3n-1), a(3n)) = (A031175(k), A031174(k), A031173(k)) for some k, n >= 1. (The order is not the same as for A031173 etc, e.g., the 5th through 8th triple have decreasing largest sides.) Also, in A031173, A031174, A031175 and others, the side naming convention is a > b > c, the opposite of here. - M. F. Hasler, Oct 11 2018
REFERENCES
Eli Maor, The Pythagorean Theorem: A 4,000-Year History, 2007, Princeton University Press, p. 134.
LINKS
CROSSREFS
Cf. A195816.
See A245616 for a very similar sequence.
Sequence in context: A036198 A094128 A340178 * A245616 A264446 A039441
KEYWORD
nonn
AUTHOR
STATUS
approved