A165416 Irregular array read by rows: The n-th row contains those distinct positive integers that each, when written in binary, occurs as a substring in binary n.

1, 1, 2, 1, 3, 1, 2, 4, 1, 2, 5, 1, 2, 3, 6, 1, 3, 7, 1, 2, 4, 8, 1, 2, 4, 9, 1, 2, 5, 10, 1, 2, 3, 5, 11, 1, 2, 3, 4, 6, 12, 1, 2, 3, 5, 6, 13, 1, 2, 3, 6, 7, 14, 1, 3, 7, 15, 1, 2, 4, 8, 16, 1, 2, 4, 8, 17, 1, 2, 4, 9, 18, 1, 2, 3, 4, 9, 19, 1, 2, 4, 5, 10, 20, 1, 2, 5, 10, 21, 1, 2, 3, 5, 6, 11, 22, 1

Offset

1,3

Comments

This is sequence A119709 with the 0's removed.

The n-th row of this sequence contains A122953(n) terms.

Links

Reinhard Zumkeller, Rows n = 1..512 of table, flattened

Example

6 in binary is 110. The distinct positive integers that occur as substrings in n when they and n are written in binary are: 1 (1 in binary), 2 (10 in binary), 3 (11 in binary), and 6 (110 in binary). So row 6 is (1,2,3,6).

Prog

(Haskell)
a165416 n k = a165416_tabf !! (n-1) !! (k-1)
a165416_row n = a165416_tabf !! (n-1)
a165416_tabf = map (dropWhile (== 0)) $ tail a119709_tabf
-- Reinhard Zumkeller, Aug 14 2013

Crossrefs

Cf. A119709, A122953.

Cf. A030308.

Cf. A165153 (row products), A225243 (subsequence).

Sequence in context: A304038 A366113 A301983 * A222818 A057059 A368313

Adjacent sequences: A165413 A165414 A165415 * A165417 A165418 A165419

Keyword

base,nonn,tabf,look

Author

Leroy Quet, Sep 17 2009

Extensions

Extended by Ray Chandler, Mar 13 2010

Status

approved