A338338 Lexicographically earliest infinite sequence of distinct positive numbers such that for any prime p, any run of consecutive multiples of p has length exactly 3.

1, 2, 4, 6, 3, 9, 5, 10, 20, 8, 7, 14, 28, 12, 15, 30, 40, 16, 11, 22, 44, 18, 21, 42, 56, 24, 27, 33, 55, 110, 50, 26, 13, 39, 36, 48, 32, 17, 34, 68, 38, 19, 57, 45, 60, 70, 84, 63, 51, 85, 170, 80, 46, 23, 69, 54, 66, 88, 77, 35, 105, 75, 72, 52, 78, 117

Offset

1,2

Comments

If a prime p divides a(n), then there is a run of exactly three terms (one of which is a(n)) that are divisible by p.

If "three" is changed to "two", we get A280864.

Conjecture: This is a permutation of the positive integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..20000

Rémy Sigrist, PARI program for A338338

Example

After 1,2,4,6,3, we have had two successive multiples of 3, so the next term must be a multiple of 3 we have not yet seen, hence 9. The following term is then the smallest number not yet seen which is not a multiple of 3, hence 5.

Prog

(PARI) See Links section.

Crossrefs

A338339-A338349, A338440, A338449, A338450, and A338451 analyze this sequence from various points of view.

Cf. A280864, A338441.

Sequence in context: A181473 A181548 A207779 * A350927 A362015 A096665

Adjacent sequences: A338335 A338336 A338337 * A338339 A338340 A338341

Keyword

nonn

Author

N. J. A. Sloane, Oct 27 2020

Extensions

Corrected and extended by Rémy Sigrist, Oct 27 2020

Status

approved