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

Author

Rémy Sigrist, Nov 16 2024

Keywords

• nonn
• base

Comments

Will every integer appear in the sequence?

Examples

			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
		

Links

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

Crossrefs

See A342072 and A378106 for similar sequences.

Programs

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