A338804 A sequence containing each nonnegative integer exactly twice, such that for all k, k numbers appear in the sequence between the first and second appearances of k.

0, 0, 3, 1, 2, 1, 3, 2, 9, 10, 11, 12, 4, 5, 6, 7, 8, 4, 9, 5, 10, 6, 11, 7, 12, 8, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 13, 27, 14, 28, 15, 29, 16, 30, 17, 31, 18, 32, 19, 33, 20, 34, 21, 35, 22, 36, 23, 37, 24, 38, 25, 39, 26

Offset: 1

Author

Elliott Line, Nov 10 2020

Keywords

• nonn
• easy

Comments

The sequence is constructed so that after the initial two 0's the next three pairs form a self-contained block beginning with 3, the subsequent nine pairs form a self-contained block beginning with 9, the following twenty-seven pairs form a block beginning with 27, etc. (powers of 3: A000244).

There are numerous sequences that satisfy the given criteria, so to fully define the continuation of this sequence I will add the following extra constraints. After the 0th block 0,0 the n-th block is found as follows: The block can be split into two halves such that one occurrence of each number appears in each half. The first half of the n-th block begins with 3^n then increases by consecutive integers until the maximum for that block: (3^(n+1) - 3)/2, before abruptly dropping to (3^n - 1)/2 and increasing by consecutive integers until (3^n - 1) is reached. The second half of the n-th block is then defined by the original constraints.

Examples

			From the first and second appearances of 5 the sequence is 5, 6, 7, 8, 4, 9, 5 and as such has five numbers between the two 5's.
		

Crossrefs

Cf. A000244, A026272.