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

1,4

Comments

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

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A011782, A070939, A342585, A356784, A358121.

Sequence in context: A062050 A358086 A358066 * A357443 A233782 A233972

Adjacent sequences: A358082 A358083 A358084 * A358086 A358087 A358088

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Oct 30 2022

Status

approved