A338339 -id:A338339 - cp's OEIS frontend

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

N. J. A. Sloane, Oct 27 2020

nonn

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.

			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.

Rémy Sigrist, Table of n, a(n) for n = 1..20000
Rémy Sigrist, PARI program for A338338

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

Cf. A280864, A338441.

PARI
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Corrected and extended by Rémy Sigrist, Oct 27 2020

A338346 1, followed by first differences of A338340.

Original entry on oeis.org

1, 5, 4, 8, 19, 40, 4, 9, 34, 32, 4, 25, 20, 54, 30, 41, 46, 53, 23, 40, 9, 12, 87, 9, 9, 56, 9, 27, 33, 53, 25, 124, 93, 22, 26, 128, 98, 4, 177, 63, 179, 29, 165, 9, 114, 164, 14, 29, 262, 188, 9, 127, 58, 10, 10, 58, 30, 97, 268, 229, 223, 28, 9, 97, 62, 9, 67, 87, 43, 52

Offset: 1

N. J. A. Sloane, Oct 27 2020

nonn

A338338 has a natural division into blocks, where the blocks (after the initial 1) start at the primes described in A338339 and A338340. The first few blocks are
[1], [2, 4, 6, 3, 9], [5, 10, 20, 8], [7, 14, 28, 12, 15, 30, 40, 16], [11, 22, 44, 18, ..., 36, 48, 32], [17, ...
and the present sequence gives the lengths of the successive blocks.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A338338-A338349.

cp's OEIS Frontend

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.

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