A378107 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, either a(n+1) is a multiple of a(n) or the decimal expansion of a(n+1) appears in that of a(n).

1, 2, 4, 8, 16, 6, 12, 24, 48, 96, 9, 18, 36, 3, 15, 5, 10, 20, 40, 80, 160, 60, 120, 240, 480, 960, 1920, 19, 38, 76, 7, 14, 28, 56, 112, 11, 22, 44, 88, 176, 17, 34, 68, 136, 13, 26, 52, 104, 208, 416, 41, 82, 164, 64, 128, 256, 25, 50, 100, 200, 400, 800

Offset

1,2

Comments

Will every integer appear in the sequence?

Links

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

Rémy Sigrist, PARI program

Example

The first terms are:
  n   a(n)
  --  ----
   1     1
   2     2
   3     4
   4     8
   5    16
   6     6      (6 appears in 16)
   7    12
   8    24
   9    48
  10    96
  11     9      (9 appears in 96)
  12    18
  13    36
  14     3      (3 appears in 36)
  15    15

Prog

(PARI) \\ See Links section.
(Python)
from itertools import combinations, count, islice
def agen(): # generator of terms
    an, aset = 1, {0, 1}
    while True:
        yield an
        s = str(an)
        subs = (int(s[i:j]) for i, j in combinations(range(len(s)+1), 2))
        an1 = min((t for t in subs if t not in aset), default=-1)
        if an1 == -1:
            an = next(k*an for k in count(2) if k*an not in aset)
        else:
            an = an1
        aset.add(an)
print(list(islice(agen(), 62))) # Michael S. Branicky, Nov 17 2024

Crossrefs

See A342072 and A378106 for similar sequences.

Sequence in context: A306601 A237851 A167425 * A212638 A016018 A333492

Adjacent sequences: A378104 A378105 A378106 * A378108 A378109 A378110

Keyword

nonn,base

Author

Rémy Sigrist, Nov 16 2024

Status

approved