A394858 Lexicographically earliest sequence of distinct positive integers such that for any n > 1, the prime tower factorizations of a(n) and a(n+1) have some common prime number.

1, 2, 4, 6, 3, 8, 9, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, 33, 24, 25, 26, 13, 39, 27, 30, 28, 32, 34, 17, 51, 36, 38, 19, 57, 40, 35, 42, 44, 45, 46, 23, 69, 48, 49, 50, 52, 54, 56, 58, 29, 87, 60, 55, 65, 70, 62, 31, 93, 63, 64, 66, 68, 72, 74, 37

Offset

1,2

Comments

The prime tower factorization of a number is defined in A182318.

A variant of the EKG sequence (A064413).

Links

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

Rémy Sigrist, PARI program

Example

The first terms are:
  n   a(n)  a(n)-th row of A336964
  --  ----  ----------------------
   1     1  [1]
   2     2  [2]
   3     4  [2]
   4     6  [2, 3]
   5     3  [3]
   6     8  [2, 3]
   7     9  [2, 3]
   8    10  [2, 5]
   9     5  [5]
  10    15  [3, 5]
  11    12  [2, 3]
  12    14  [2, 7]
  13     7  [7]
  14    21  [3, 7]
  15    18  [2, 3]
  16    16  [2]
  17    20  [2, 5]
  18    22  [2, 11]
  19    11  [11]
  20    33  [3, 11]

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A064413, A182318, A394857.

Sequence in context: A089088 A251622 A073899 * A232846 A381098 A101543

Adjacent sequences: A394855 A394856 A394857 * A394859 A394860 A394861

Keyword

nonn

Author

Rémy Sigrist, Apr 04 2026

Status

approved