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A330647 Lexicographically earliest sequence of distinct positive terms with an associate sequence t such that a(1) = t(1) = 1 and for n > 1, either a(n) divides t(n-1) (and in that case set t(n) = t(n-1)/a(n)) or a(n) is coprime to t(n-1) (and in that case set t(n) = t(n-1)*a(n)). 2
1, 2, 3, 5, 6, 4, 7, 9, 10, 11, 13, 14, 8, 12, 17, 19, 22, 16, 23, 24, 15, 26, 28, 20, 21, 18, 25, 29, 30, 31, 32, 34, 37, 38, 40, 35, 41, 43, 44, 33, 27, 36, 47, 52, 39, 46, 51, 42, 48, 49, 53, 56, 58, 59, 61, 64, 60, 45, 62, 63, 57, 67, 68, 71, 73, 74, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All prime numbers appear in the sequence, in ascending order.

This sequence is likely a permutation of the natural numbers.

LINKS

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

Rémy Sigrist, Scatterplot of (n, a(n)-n) for n = 1..250000

Rémy Sigrist, PARI program for A330647

EXAMPLE

The first terms, alongside the corresponding t(n), are:

  n   a(n)  t(n)

  --  ----  ----

   1     1     1

   2     2     2

   3     3     6

   4     5    30

   5     6     5

   6     4    20

   7     7   140

   8     9  1260

   9    10   126

  10    11  1386

MATHEMATICA

Nest[Append[#1, Block[{k = 2, s}, While[Nand[FreeQ[#1[[All, 1]], k], MemberQ[{1, k}, Set[s, GCD[#3, k]]]], k++]; {k, If[s == 1, #3 k, #3/k]}]] & @@ {#, #[[-1, 1]], #[[-1, -1]]} &, {{1, 1}}, 66][[All, 1]] (* Michael De Vlieger, Dec 23 2019 *)

PROG

(PARI) See Links section.

CROSSREFS

See A330648 for the corresponding sequence t.

Cf. A008336.

Sequence in context: A130951 A130386 A294269 * A209260 A297409 A335858

Adjacent sequences:  A330644 A330645 A330646 * A330648 A330649 A330650

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Dec 22 2019

STATUS

approved

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Last modified September 24 12:31 EDT 2021. Contains 347642 sequences. (Running on oeis4.)