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A280945 List of primitive triples (x, y, z) of positive integers for which xy - z, yz - x, and zx - y are powers of 2. 0
2, 2, 2, 2, 2, 3, 2, 6, 11, 3, 5, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are sixteen such triples, namely (2, 2, 2), the three permutations of (2, 2, 3), and the six permutations of each of (2, 6, 11) and (3, 5, 7).

See the proof in the link.

The sixteen triples are (2, 2, 2), (2, 2, 3), (2, 3, 2), (3, 2, 2), (2, 6, 11), (2, 11, 6), (6, 2, 11), (6, 11, 2), (11, 2, 6), (11, 6, 2), (3, 5, 7), (3, 7, 5), (5, 3, 7), (5, 7, 3), (7, 3, 5) and (7, 5, 3).

LINKS

Table of n, a(n) for n=1..12.

56th International Mathematical Olympiad, Problem N5

EXAMPLE

The 3th primitive triple (x, y, z) = (2, 6, 11) is in the sequence because xy - z = 1, yz - x = 2^6 and zx - y = 2^4.

CROSSREFS

Sequence in context: A165054 A067743 A029230 * A196067 A251141 A319696

Adjacent sequences:  A280942 A280943 A280944 * A280946 A280947 A280948

KEYWORD

nonn,fini,full,tabf

AUTHOR

Michel Lagneau, Jan 11 2017

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)