A119709 Table where n-th row (of A078822(n) terms) contains the distinct nonnegative integers which, when written in binary, are substrings of n written in binary.

0, 1, 0, 1, 2, 1, 3, 0, 1, 2, 4, 0, 1, 2, 5, 0, 1, 2, 3, 6, 1, 3, 7, 0, 1, 2, 4, 8, 0, 1, 2, 4, 9, 0, 1, 2, 5, 10, 0, 1, 2, 3, 5, 11, 0, 1, 2, 3, 4, 6, 12, 0, 1, 2, 3, 5, 6, 13, 0, 1, 2, 3, 6, 7, 14, 1, 3, 7, 15, 0, 1, 2, 4, 8, 16, 0, 1, 2, 4, 8, 17, 0, 1, 2, 4, 9, 18, 0, 1, 2, 3, 4, 9, 19, 0, 1, 2, 4, 5, 10

Offset: 0

Author

Leroy Quet, Jun 10 2006

Keywords

• tabf
• easy
• nonn
• look

Examples

			12 in binary is 1100. Within this binary representation there is 0 (occurring twice), 1 (occurring twice), 10 (= 2 in decimal), 11 (= 3 in decimal), 100 (= 4 in decimal), 110 (= 6 in decimal) and 1100 (= 12 in decimal).
So row 12 = (0,1,2,3,4,6,12).
		

Links

• Reinhard Zumkeller, Rows n = 0..511 of table, flattened

Crossrefs

Cf. A078822.

Cf. A030308, A165416.

Programs

Haskell

import Data.List (isInfixOf)
a119709 n k = a119709_tabf !! n !! k
a119709_row n = map (foldr (\d v -> v * 2 + toInteger d) 0) $
   filter (`isInfixOf` (a030308_row n)) $ take (n + 1) a030308_tabf
a119709_tabf = map a119709_row [0..]
-- Reinhard Zumkeller, Aug 14 2013

Extensions

Extended by Ray Chandler, Mar 13 2010