

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.


10



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: A144113 A304038 A301983 * 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



