A358120 -id:A358120 - cp's OEIS frontend

A358124 Distinct values of A358120, in order of appearance.

1, 2, 3, 4, 5, 6, 8, 7, 9, 13, 11, 10, 12, 14, 20, 18, 21, 16, 15, 19, 17, 22, 32, 30, 34, 26, 33, 24, 28, 23, 29, 27, 31, 25, 35, 51, 47, 55, 43, 53, 49, 52, 39, 54, 37, 45, 41, 36, 46, 44, 50, 40, 48, 38, 42, 56, 82, 76, 88, 72, 86, 80, 89, 64, 84, 78, 83

Offset: 1

Rémy Sigrist, Oct 30 2022

nonn

This sequence is a permutation of the positive integers with inverse A358143.

Rémy Sigrist, Table of n, a(n) for n = 1..10946
Rémy Sigrist, Scatterplot of the first 832040 terms
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A358120, A358143.

PARI
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A358090 Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-2 and n-1 flattened.

Original entry on oeis.org

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

Offset: 1

Rémy Sigrist, Oct 30 2022

This sequence is a variant of A356784; here we consider two prior rows, there all prior rows, hence the term "partial" in the name.

The n-th row contains A000045(n) terms, and is a permutation of 1..A000045(n).

			Table begins:
    1,
    1,
    1, 2,
    1, 2, 3,
    1, 3, 2, 4, 5,
    1, 4, 2, 6, 3, 5, 7, 8,
    1, 6, 3, 8, 2, 10, 4, 7, 5, 11, 9, 12, 13,
    ...
For n = 7:
- the terms in rows 5 and 6 are: 1, 3, 2, 4, 5, 1, 4, 2, 6, 3, 5, 7, 8,
- positions of 1's are: 1, 6,
- positions of 2's are: 3, 8,
- positions of 3's are: 2, 10,
- positions of 4's are: 4, 7,
- positions of 5's are: 5, 11,
- positions of 6's are: 9,
- positions of 7's are: 12,
- positions of 8's are: 13,
- so row 7 is: 1, 6, 3, 8, 2, 10, 4, 7, 5, 11, 9, 12, 13.

Rémy Sigrist, Table of n, a(n) for n = 1..10945
Rémy Sigrist, Scatterplot of the first 832039 terms
Rémy Sigrist, PARI program

See A358120 for a similar sequence.

Cf. A000045, A001611, A342585, A356784, A358123.

PARI
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See Links section.
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T(n, 1) = 1.

T(n, 2) = A001611(n-2) for n > 2.

cp's OEIS Frontend

A358124 Distinct values of A358120, in order of appearance.

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