

A165416


Irregular array read by rows: The nth row contains those distinct positive integers that each, when written in binary, occurs as a substring in binary n.


9



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

This is sequence A119709 with the 0's removed.
The nth row of this sequence contains A122953(n) terms.


LINKS

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


EXAMPLE

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).


PROG

(Haskell)
a165416 n k = a165416_tabf !! (n1) !! (k1)
a165416_row n = a165416_tabf !! (n1)
a165416_tabf = map (dropWhile (== 0)) $ tail a119709_tabf
 Reinhard Zumkeller, Aug 14 2013


CROSSREFS

Cf. A119709, A122953.
Cf. A030308.
Cf. A165153 (row products), A225243 (subsequence).
Sequence in context: A089384 A228812 A144113 * A222818 A057059 A169896
Adjacent sequences: A165413 A165414 A165415 * A165417 A165418 A165419


KEYWORD

base,nonn,tabf,look


AUTHOR

Leroy Quet, Sep 17 2009


EXTENSIONS

Extended by Ray Chandler, Mar 13 2010


STATUS

approved



