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

0,5

Links

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

Example

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).

Prog

(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

Crossrefs

Cf. A078822.

Cf. A030308, A165416.

Sequence in context: A140256 A126206 A307744 * A328167 A253556 A252735

Adjacent sequences: A119706 A119707 A119708 * A119710 A119711 A119712

Keyword

tabf,easy,nonn,look

Author

Leroy Quet, Jun 10 2006

Extensions

Extended by Ray Chandler, Mar 13 2010

Status

approved