A342072 Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, a(n+1) can be obtained by replacing in the decimal representation of a(n) some nonempty substring m (without leading zero) by a divisor of m or by a positive multiple of m.

1, 2, 4, 8, 16, 11, 12, 3, 6, 18, 9, 27, 17, 34, 14, 7, 21, 22, 24, 28, 48, 41, 42, 44, 84, 81, 82, 86, 26, 13, 19, 29, 23, 43, 46, 92, 32, 31, 33, 36, 66, 61, 62, 64, 68, 38, 76, 71, 72, 74, 37, 67, 127, 47, 87, 167, 117, 39, 69, 63, 123, 113, 111, 112, 56

Offset: 1

Author

Rémy Sigrist, Feb 27 2021

Keywords

• nonn
• base

Comments

The procedure used to generate the terms of this sequence has similarities with that described in A323286 (Choix de Bruxelles); however here, we don't limit ourselves to divide or multiply by two.

Apparently, all positive integers appear in this sequence.

Multiples of 5 are clustered.

Examples

			The first terms, alongside the substitution that gives a(n+1), are:
  n   a(n)  a(n+1)
  --  ----  ------
   1     1   (1*2)
   2     2   (2*2)
   3     4   (4*2)
   4     8   (8*2)
   5    16  1(6/6)
   6    11  1(1*2)
   7    12  (12/4)
   8     3   (3*2)
   9     6   (6*3)
  10    18  (18/2)
  11     9   (9*3)
  12    27  (2/2)7
  13    17  (17*2)
  14    34  (3/3)4
  15    14  (14/2)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored scatterplot of the first 10000 terms (red pixels correspond to five clusters of multiples of 5)
• Rémy Sigrist, PARI program for A342072

Crossrefs

Cf. A323286.

Programs

PARI

See Links section.