A278962 Each triple of consecutive terms contains a term that divides the product of the other two terms.

1, 2, 3, 4, 6, 8, 9, 12, 15, 5, 7, 10, 14, 20, 21, 28, 16, 24, 18, 27, 22, 11, 13, 26, 17, 34, 19, 38, 23, 46, 25, 50, 29, 58, 30, 45, 32, 36, 40, 48, 35, 42, 49, 54, 63, 56, 64, 70, 80, 72, 60, 55, 33, 39, 44, 52, 65, 68, 85, 75, 51, 100, 102, 120, 90, 57, 76

Offset: 1

Author

Rémy Sigrist, Dec 02 2016

Keywords

• nonn

Comments

This is the lexicographically first sequence of distinct terms with this property.

Conjectures:

- All primes appear, and in increasing order,

- If a(i) is prime and i

Here are some triples of consecutive terms where each term divides the product of the two others:

- (a(99), a(100), a(101)) = (132, 143, 156) = (2^2*3*11, 11*13, 2^2*3*13),

- (a(5714), a(5715), a(5716)) = (7055, 5146, 5270) = (5*17*83, 2*31*83, 2*5*17*31),

- (a(6674), a(6675), a(6676)) = (8099, 6052, 6188) = (7*13*89, 2^2*17*89, 2^2*7*13*17).

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A278962

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