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

Author

Leroy Quet, Sep 17 2009

Keywords

• base
• nonn
• tabf
• look

Comments

This is sequence A119709 with the 0's removed.

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

Examples

			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).
		

Links

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

Crossrefs

Cf. A119709, A122953.

Cf. A030308.

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

Programs

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

Extensions

Extended by Ray Chandler, Mar 13 2010