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

1,2

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.

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

Example

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)

Prog

(PARI) See Links section.

Crossrefs

Cf. A323286.

Sequence in context: A167421 A020954 A070347 * A095915 A208278 A036120

Adjacent sequences: A342069 A342070 A342071 * A342073 A342074 A342075

Keyword

nonn,base

Author

Rémy Sigrist, Feb 27 2021

Status

approved