A331010 -id:A331010 - cp's OEIS frontend

A331016 Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has max(1, A001221(a(n))) terms and for n > 1, T(n, k) is a multiple of the k-th prime factor of a(n) (=A027748(a(n), k)).

1, 2, 3, 4, 5, 6, 9, 12, 8, 15, 10, 18, 20, 14, 25, 16, 21, 22, 30, 24, 7, 35, 26, 27, 28, 32, 11, 34, 33, 40, 36, 39, 42, 45, 49, 38, 13, 48, 44, 56, 46, 55, 50, 17, 51, 66, 52, 60, 54, 57, 63, 65, 58, 69, 70, 72, 75, 77, 62, 19, 78, 64, 81, 68, 88, 74, 84

Offset: 1

Rémy Sigrist, Jan 06 2020

This sequence is a permutation of the natural numbers:
- beyond the sixth row, every even number gives rise to another even number,
- so eventually every even number appears in the sequence,
- for any odd prime number p we will have infinitely many multiples of 2*p,
- giving rise to infinitely many multiples of p,
- and eventually every number will appear.

			The first terms and rows are:
  n   a(n)  row(n)
  --  ----  ------------
   1     1  [1]
   2     2  [2]
   3     3  [3]
   4     4  [4]
   5     5  [5]
   6     6  [6, 9]
   7     9  [12]
   8    12  [8, 15]
   9     8  [10]
  10    15  [18, 20]
  11    10  [14, 25]

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A331016
Index entries for sequences that are permutations of the natural numbers

See A331010 for similar sequences.

Cf. A001221, A027748.

PARI
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A331018 Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has a(n) terms and for n > 1, T(n, k) is a multiple of k.

Original entry on oeis.org

1, 2, 4, 3, 6, 9, 8, 5, 10, 12, 7, 14, 15, 16, 20, 18, 11, 22, 21, 24, 25, 30, 28, 32, 27, 13, 26, 33, 36, 35, 42, 49, 40, 17, 34, 39, 44, 45, 19, 38, 48, 52, 50, 54, 56, 64, 63, 60, 23, 46, 51, 68, 55, 66, 70, 72, 81, 80, 77, 84, 29, 58, 57, 76, 65, 78, 91

Offset: 1

Rémy Sigrist, Jan 07 2020

This sequence is a permutation of the natural numbers as each row starts with the least value not yet in the sequence.

			The first terms and rows are:
  n   a(n)  row(n)
  --  ----  -------------------------------------
   1     1  [1]
   2     2  [2, 4]
   3     4  [3, 6, 9, 8]
   4     3  [5, 10, 12]
   5     6  [7, 14, 15, 16, 20, 18]
   6     9  [11, 22, 21, 24, 25, 30, 28, 32, 27]
   7     8  [13, 26, 33, 36, 35, 42, 49, 40]
   8     5  [17, 34, 39, 44, 45]
   9    10  [19, 38, 48, 52, 50, 54, 56, 64, 63, 60]
  10    12  [23, 46, 51, 68, 55, 66, 70, 72, 81, 80, 77, 84]
  11     7  [29, 58, 57, 76, 65, 78, 91]

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers
Rémy Sigrist, PARI program for A331018

See A331010 for similar sequences.

PARI
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See Links section.
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A331026 Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the n-th nonzero decimal digit in the sequence divides the n-th term.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 16, 20, 17, 25, 19, 24, 21, 30, 22, 23, 28, 26, 35, 27, 36, 32, 40, 34, 29, 33, 38, 42, 44, 39, 46, 48, 50, 54, 45, 55, 52, 49, 51, 60, 57, 56, 64, 63, 68, 58, 72, 66, 69, 75, 80, 76, 62, 84, 88, 78, 81

Offset: 1

Rémy Sigrist, Jan 07 2020

This sequence is a permutation of the natural numbers:
- necessarily some nonzero digit, say d, appears infinitely many times,
- if d=1, then we have infinitely many multiples of 1, and eventually every number will show up,
- if d>1, then all the multiples of d will show up, as there are infinitely many multiples of d containing a "1" digit, we have infinitely many multiples of 1 as well, and eventually every number will show up.
This sequence can also be seen as an irregular table, where the n-th has A055640(a(n)) terms, and T(n, k) is a multiple of the k-th nonzero digit of a(n).

			For first terms and corresponding digits are:
  n   a(n)  n-th digit
  --  ----  ----------
   1     1           1
   2     2           2
   3     3           3
   4     4           4
   5     5           5
   6     6           6
   7     7           7
   8     8           8
   9     9           9
  10    10           1
  11    11           1
  12    12           1
  13    13           1
  14    14           2

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A331026
Index entries for sequences that are permutations of the natural numbers

See A331010 for similar sequences.

Cf. A055640.

PARI
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cp's OEIS Frontend

A331016 Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has max(1, A001221(a(n))) terms and for n > 1, T(n, k) is a multiple of the k-th prime factor of a(n) (=A027748(a(n), k)).

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A331018 Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has a(n) terms and for n > 1, T(n, k) is a multiple of k.

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PARI

A331026 Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the n-th nonzero decimal digit in the sequence divides the n-th term.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI