A358086 Inventory of positions ordered by odd parts of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with odd part 1, followed by positions of terms with odd part 3, 5, etc. in prior rows flattened.

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

Offset: 1

Author

Rémy Sigrist, Oct 30 2022

Keywords

• nonn
• tabf

Comments

The n-th row contains A011782(n-1) terms, and is a permutation of 1..A011782(n-1).

Examples

			Table begins:
    1,
    1,
    1, 2,
    1, 2, 3, 4,
    1, 2, 3, 4, 5, 6, 8, 7,
    1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 7, 11, 14, 13, 16,
    ...
For n = 6:
the terms in rows 1..5 are: 1, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 8, 7,
- terms with odd part 1 are at positions: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15,
- terms with odd part 3 are at positions: 7, 11, 14,
- terms with odd part 5 are at positions: 13,
- terms with odd part 7 are at positions: 16,
- so row 6 is: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 7, 11, 14, 13, 16.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, PARI program
• Rémy Sigrist, Scatterplot of the first 2^20 terms

Crossrefs

Cf. A000265, A011782, A342585, A356784, A358085, A358122.

Programs

PARI

See Links section.