A385661 Lexicographically earliest sequence of distinct positive integers that can be partitioned into runs of pairwise coprime integers, the n-th such run having a(n) terms.

1, 2, 3, 4, 5, 7, 6, 11, 13, 17, 8, 9, 19, 23, 25, 10, 21, 29, 31, 37, 41, 43, 12, 35, 47, 53, 59, 61, 14, 15, 67, 71, 73, 79, 83, 89, 97, 101, 103, 16, 27, 49, 55, 107, 109, 113, 127, 131, 137, 139, 149, 151, 18, 65, 77, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229

Offset

1,2

Comments

This sequence is a permutation of the positive integers as each run starts with the least integer not yet in the sequence.

The prime numbers appear in natural order.

Links

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

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, 1) = 2*n-2 for any n > 1.

Example

The first terms and runs are:
  n   a(n)  n-th run
  --  ----  -----------------------------------------------------------
   0     1  1
   1     2  2, 3
   3     3  4, 5, 7
   6     4  6, 11, 13, 17
  10     5  8, 9, 19, 23, 25
  15     7  10, 21, 29, 31, 37, 41, 43
  22     6  12, 35, 47, 53, 59, 61
  28    11  14, 15, 67, 71, 73, 79, 83, 89, 97, 101, 103
  39    13  16, 27, 49, 55, 107, 109, 113, 127, 131, 137, 139, 149, 151

Prog

(PARI) \\ See Links section.

Crossrefs

See A386932 for a similar sequence.

Cf. A076034, A385735 (inverse).

Sequence in context: A080688 A082025 A076034 * A336349 A255545 A034152

Adjacent sequences: A385658 A385659 A385660 * A385662 A385663 A385664

Keyword

nonn,tabf

Author

Rémy Sigrist, Aug 09 2025

Status

approved