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)).

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

Offset: 1

Author

Rémy Sigrist, Dec 22 2019

Keywords

• nonn

Comments

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

This sequence is likely a permutation of the natural numbers.

Examples

			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
		

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

Crossrefs

See A330648 for the corresponding sequence t.

Cf. A008336.

Programs

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 *)

PARI

See Links section.