A165416 - OEIS

%I #15 Jul 17 2015 05:56:44

%S 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,

%T 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,

%U 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

%N 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.

%C This is sequence A119709 with the 0's removed.

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

%H Reinhard Zumkeller, <a href="/A165416/b165416.txt">Rows n = 1..512 of table, flattened</a>

%e 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).

%o (Haskell)

%o a165416 n k = a165416_tabf !! (n-1) !! (k-1)

%o a165416_row n = a165416_tabf !! (n-1)

%o a165416_tabf = map (dropWhile (== 0)) $ tail a119709_tabf

%o -- _Reinhard Zumkeller_, Aug 14 2013

%Y Cf. A119709, A122953.

%Y Cf. A030308.

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

%K base,nonn,tabf,look

%O 1,3

%A _Leroy Quet_, Sep 17 2009

%E Extended by _Ray Chandler_, Mar 13 2010