A355435 Lexicographically earliest sequence of distinct positive integers such that for any n > 1, a(n) is a multiple of a(A080079(n-1)).

1, 2, 4, 3, 6, 8, 10, 5, 15, 20, 16, 12, 9, 24, 14, 7, 21, 28, 48, 18, 36, 32, 40, 30, 25, 50, 56, 42, 27, 44, 22, 11, 33, 66, 88, 54, 84, 112, 100, 75, 60, 80, 64, 72, 90, 96, 140, 63, 35, 70, 120, 45, 108, 128, 160, 105, 55, 110, 104, 78, 39, 52, 26, 13

Offset: 1

Author

Rémy Sigrist, Jul 02 2022

Keywords

• nonn
• tabf

Comments

This sequence is a permutation of the positive integers with inverse A355436.

The construction of this sequence is similar to that of A269838.

This sequence can also be seen as an irregular table:

- with row lengths given by A011782,

- with initial row (1),

- given the first k+1 rows (with globally 2^k terms), the next row contains a multiple of a(2^k), followed by a multiple of a(2^k-1), ..., followed by a multiple of a(1).

Examples

			As an irregular table, the first rows are:
    [1]
    [2]
    [4, 3]
    [6, 8, 10, 5]
    [15, 20, 16, 12, 9, 24, 14, 7]
    [21, 28, 48, 18, 36, 32, 40, 30, 25, 50, 56, 42, 27, 44, 22, 11]
.
The first terms are:
  n   a(n)  A080079(n-1)  a(A080079(n-1))
  --  ----  ------------  ---------------
   1     1  N/A           N/A
   2     2             1                1
   3     4             2                2
   4     3             1                1
   5     6             4                3
   6     8             3                4
   7    10             2                2
   8     5             1                1
   9    15             8                5
  10    20             7               10
  11    16             6                8
  12    12             5                6
  13     9             4                3
  14    24             3                4
  15    14             2                2
  16     7             1                1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A011782, A080079, A269838, A355436 (inverse).

Programs

PARI

See Links section.

Formula

a(2^n) = prime(n) for any n > 0 (where prime(n) denotes the n-th prime number).