A357443 Inventory sequence, second version: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1.

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

Offset

1,4

Comments

Essentially the same as A358066, except that at stage k we record where all the numbers from 1 to 2^k have appeared in the sequence in earlier stages. (In A358066 we only look at where the numbers from 1 to k have appeared.)

This means that when the sequence is displayed as a triangle, the row corresponding to stage k >= 1 is a permutation of the numbers from 1 to 2^k.

Links

Table of n, a(n) for n=1..76.

Formula

a(n) = A356784(n-1) + 1. - Rémy Sigrist, Nov 08 2022

Example

As an irregular triangle, the sequence begins:
1, 1,
1, 2,
1, 2, 3, 4,
1, 2, 3, 5, 4, 6, 7, 8,
1, 2, 3, 5, 9, 4, 6, 10, 7, 11, 8, 13, 12, 14, 15, 16,
1, 2, 3, 5, 9, 17, 4, 6, 10, 18, 7, 11, 19, 8, 13, 22, 12, 20, 14, 23, 15, 25, 16, 27, 21, 24, 26, 29, 28, 30, 31, 32,
...

Crossrefs

Cf. A342585, A356784, A358066.

Sequence in context: A358086 A358066 A358085 * A233782 A233972 A169778

Adjacent sequences: A357440 A357441 A357442 * A357444 A357445 A357446

Keyword

nonn,tabf

Author

Ctibor O. Zizka, Oct 29 2022, edited by N. J. A. Sloane, Nov 07 2022. (Because of a missing term in the initial submission, the definition could be interpreted in two ways: A358066 was the first interpretation, this is the second.)

Extensions

More terms from Rémy Sigrist, Nov 08 2022

Status

approved