A358085 Inventory of positions ordered by binary lengths of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with binary length 1, followed by positions of terms with binary length 2, 3, etc. in prior rows flattened.

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

Offset: 1

Author

Rémy Sigrist, Oct 30 2022

Keywords

• nonn
• base
• 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, 5, 4, 6, 7, 8,
    1, 2, 3, 5, 9, 4, 6, 7, 10, 11, 8, 12, 13, 14, 15, 16,
    ...
For n = 6:
- the terms in rows 1..5 are: 1, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 5, 4, 6, 7, 8,
- terms with binary length 1 are at positions: 1, 2, 3, 5, 9,
- terms with binary length 2 are at positions: 4, 6, 7, 10, 11,
- terms with binary length 3 are at positions: 8, 12, 13, 14, 15,
- terms with binary length 4 are at positions: 16,
- so row 6 is: 1, 2, 3, 5, 9, 4, 6, 7, 10, 11, 8, 12, 13, 14, 15, 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. A011782, A070939, A342585, A356784, A358121.

Programs

PARI

See Links section.