A360633 -id:A360633 - cp's OEIS frontend

A360613 Lexicographically earliest sequence of positive integers such that the products of the form a(2u-1) a(2*v) with u, v > 0 are all distinct.

1, 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 14, 17, 18, 19, 23, 24, 25, 29, 26, 31, 28, 33, 36, 37, 41, 40, 43, 47, 46, 49, 50, 51, 52, 53, 59, 55, 61, 57, 63, 64, 67, 71, 73, 79, 81, 83, 82, 85, 86, 87, 88, 89, 91, 93, 92, 95, 97, 101, 100, 103, 107, 109, 113, 111

Offset: 1

Rémy Sigrist, Feb 14 2023

nonn

In other words, the products of a term from the odd bisection by a term from the even bisection are all distinct.
If we consider the bitwise XOR operator instead of the multiplication then we obtain A000695 interleaved with A062880.
The value 1 is the only duplicate.
All prime numbers appear in this sequence, in ascending order.
For n = 1..50000, if m_n denotes the least positive value not in {a(2*u-1) * a(2*v), 1 <= 2*u-1 <= n and 1 <= 2*v <= n}, then a(n+1) = m_n or a(n+2) = m_n. Will this pattern last forever?

			The first terms, alongside the corresponding products, are:
  n   a(n)  Corresponding products
  --  ----  --------------------------
   1     1
   2     1   1
   3     2   2
   4     3   3,  6
   5     4   4, 12
   6     5   5, 10, 20
   7     7   7, 21, 35
   8     8   8, 16, 32,  56
   9     9   9, 27, 45,  72
  10    11  11, 22, 44,  77,  99
  11    13  13, 39, 65, 104, 143
  12    15  15, 30, 60, 105, 135, 195

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

Cf. A000695, A062880, A066724, A360627-A360628 (bisections), A360633 (products).

C
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See Links section.
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a(n) < a(n+2).

A360627 Odd bisection of A360613: a(n) = A360613(2*n-1).

Original entry on oeis.org

1, 2, 4, 7, 9, 13, 14, 18, 23, 25, 26, 28, 36, 41, 43, 46, 50, 52, 59, 61, 63, 67, 73, 81, 82, 86, 88, 91, 92, 97, 100, 107, 113, 117, 118, 122, 126, 134, 137, 146, 149, 151, 157, 161, 162, 163, 164, 169, 172, 175, 176, 182, 191, 193, 194, 207, 211, 214, 225

Offset: 1

Rémy Sigrist, Feb 14 2023

nonn

See A360628 for the even bisection.

The ratios between distinct terms of this sequence are all different from the ratios between distinct terms of A360628.

Rémy Sigrist, C program

Cf. A360613, A360628, A360633.

C
```
See Links section.
```

a(n) < a(n+1).

A360628 Even bisection of A360613: a(n) = A360613(2*n).

Original entry on oeis.org

1, 3, 5, 8, 11, 15, 17, 19, 24, 29, 31, 33, 37, 40, 47, 49, 51, 53, 55, 57, 64, 71, 79, 83, 85, 87, 89, 93, 95, 101, 103, 109, 111, 120, 121, 127, 131, 136, 139, 141, 145, 147, 152, 155, 159, 165, 167, 173, 179, 181, 185, 187, 192, 197, 199, 209, 213, 223, 227

Offset: 1

Rémy Sigrist, Feb 14 2023

nonn

See A360627 for the odd bisection.

Rémy Sigrist, C program

Cf. A360613, A360627, A360633.

C
```
See Links section.
```

a(n) < a(n+1).

cp's OEIS Frontend

A360613 Lexicographically earliest sequence of positive integers such that the products of the form a(2u-1) a(2*v) with u, v > 0 are all distinct.

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C

Formula

A360627 Odd bisection of A360613: a(n) = A360613(2*n-1).

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C

Formula

A360628 Even bisection of A360613: a(n) = A360613(2*n).

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C

Formula

cp's OEIS Frontend

A360613 Lexicographically earliest sequence of positive integers such that the products of the form a(2*u-1) * a(2*v) with u, v > 0 are all distinct.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

C

Formula

A360627 Odd bisection of A360613: a(n) = A360613(2*n-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

C

Formula

A360628 Even bisection of A360613: a(n) = A360613(2*n).

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Author

Keywords

Comments

Links

Crossrefs

Programs

C

Formula

A360613 Lexicographically earliest sequence of positive integers such that the products of the form a(2u-1) a(2*v) with u, v > 0 are all distinct.