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A278962 Each triple of consecutive terms contains a term that divides the product of the other two terms. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 22:18 EDT 2021. Contains 343957 sequences. (Running on oeis4.)