A360613 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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?

LINKS

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

Rémy Sigrist, C program

FORMULA

a(n) < a(n+2).

EXAMPLE

The first terms, alongside the corresponding products, are:

n a(n) Corresponding products

-- ---- --------------------------

1 1

2 1 1

3 2 2