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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. 8

%I

%S 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,

%T 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,

%U 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

%N 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.

%H Reinhard Zumkeller, <a href="/A119709/b119709.txt">Rows n = 0..511 of table, flattened</a>

%e 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).

%e So row 12 = (0,1,2,3,4,6,12).

%o (Haskell)

%o import Data.List (isInfixOf)

%o a119709 n k = a119709_tabf !! n !! k

%o a119709_row n = map (foldr (\d v -> v * 2 + toInteger d) 0) $

%o filter (`isInfixOf` (a030308_row n)) $ take (n + 1) a030308_tabf

%o a119709_tabf = map a119709_row [0..]

%o -- _Reinhard Zumkeller_, Aug 14 2013

%Y Cf. A078822.

%Y Cf. A030308, A165416.

%K tabf,easy,nonn,look

%O 0,5

%A _Leroy Quet_, Jun 10 2006

%E Extended by _Ray Chandler_, Mar 13 2010

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Last modified December 11 13:33 EST 2017. Contains 295876 sequences.