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

1,2

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<j, then a(i) < a(j).

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

Crossrefs

Sequence in context: A116621 A036407 A145807 * A122380 A033501 A336504

Adjacent sequences: A278959 A278960 A278961 * A278963 A278964 A278965

Keyword

nonn

Author

Rémy Sigrist, Dec 02 2016

Status

approved