A342072 -id:A342072 - cp's OEIS frontend

A368194 Irregular table T(n, k), n > 0, k = 1..A368195(n), read by rows: the n-th row lists the numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the decimal expansion of n by one of the divisors of m.

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 5, 10, 1, 11, 1, 2, 3, 4, 6, 11, 12, 1, 11, 13, 1, 2, 7, 11, 12, 14, 1, 3, 5, 11, 15, 1, 2, 4, 8, 11, 12, 13, 16, 1, 11, 17, 1, 2, 3, 6, 9, 11, 12, 14, 18, 1, 11, 13, 19, 1, 2, 4, 5, 10, 20

Offset: 1

Rémy Sigrist, Dec 16 2023

The n-th row starts with 1, ends with n, and contains the divisors of n (A027750).

			Table T(n, k) begins:
    1;
    1, 2;
    1, 3;
    1, 2, 4;
    1, 5;
    1, 2, 3, 6;
    1, 7;
    1, 2, 4, 8;
    1, 3, 9;
    1, 2, 5, 10;
    1, 11;
    1, 2, 3, 4, 6, 11, 12;
    1, 11, 13;
    1, 2, 7, 11, 12, 14;
    1, 3, 5, 11, 15;
    1, 2, 4, 8, 11, 12, 13, 16;
    1, 11, 17;
    1, 2, 3, 6, 9, 11, 12, 14, 18;
      ...

Rémy Sigrist, Table of n, a(n) for n = 1..16938 (rows for n = 1..1000 flattened)
Rémy Sigrist, PARI program
Index entries for sequences related to decimal expansion of n

Cf. A027750, A323286, A342072, A368195, A368313 (binary variant).

PARI
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See Links section.
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T(n, 1) = 1.

T(n, A368195(n)) = n.

A378106 Lexicographically earliest sequence of distinct positive integers such that among two consecutive terms, the least term divides a positive number whose decimal expansion appears in that of the other term.

Original entry on oeis.org

1, 2, 4, 8, 16, 3, 6, 12, 24, 48, 96, 9, 18, 36, 72, 7, 14, 28, 56, 5, 10, 20, 40, 80, 160, 15, 30, 60, 120, 240, 480, 32, 64, 128, 256, 25, 50, 100, 200, 400, 800, 1600, 75, 150, 300, 600, 1200, 2400, 4800, 192, 19, 38, 76, 152, 13, 26, 52, 104, 208, 416, 41

Offset: 1

Rémy Sigrist, Nov 16 2024

Will every integer appear in the sequence?

			The first terms are:
  n   a(n)
  --  ----
   1     1
   2     2
   3     4
   4     8
   5    16
   6     3      (3 divides 6, and 6 appears in 16)
   7     6
   8    12
   9    24
  10    48
  11    96
  12     9
  13    18
  14    36
  15    72

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

See A342072 and A378107 for similar sequences.

PARI
```
\\ See Links section.
```

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).

Original entry on oeis.org

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

Rémy Sigrist, Nov 16 2024

Will every integer appear in the sequence?

			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

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

See A342072 and A378106 for similar sequences.

PARI
```
\\ See Links section.
```

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

cp's OEIS Frontend

A368194 Irregular table T(n, k), n > 0, k = 1..A368195(n), read by rows: the n-th row lists the numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the decimal expansion of n by one of the divisors of m.

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A378106 Lexicographically earliest sequence of distinct positive integers such that among two consecutive terms, the least term divides a positive number whose decimal expansion appears in that of the other term.

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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).

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Python