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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.
19
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
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.
Sequence in context: A181473 A181548 A207779 * A350927 A362015 A374284
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 27 2020
EXTENSIONS
Corrected and extended by Rémy Sigrist, Oct 27 2020
STATUS
approved