A165419 Each a(n) is chosen so that n = sum a(k), for all n >= 0, where k is over the distinct nonnegative values of the substrings in binary n.

0, 1, 1, 2, 2, 3, 2, 4, 4, 5, 5, 4, 4, 4, 4, 8, 8, 9, 9, 8, 8, 11, 9, 8, 8, 8, 8, 10, 8, 8, 8, 16, 16, 17, 17, 16, 18, 16, 17, 16, 16, 16, 21, 16, 16, 19, 17, 16, 16, 16, 16, 18, 16, 16, 18, 16, 16, 16, 16, 16, 16, 16, 16, 32, 32, 33, 33, 32, 34, 32, 33, 32, 32, 37, 32, 32, 34, 32, 33

Offset

0,4

Comments

We could have instead taken k over the distinct positive values of the substrings in binary n, and get the same sequence, since a(0)=0.

The distinct nonnegative values of the substrings of binary n is row n of table A119709. The distinct positive values of the substrings of binary n is row n of table A165416.

Links

Table of n, a(n) for n=0..78.

Example

9 in binary is 1001. The distinct nonnegative integers that occur as substrings in binary 9 are 0, 1, 2 (10 in binary), 4 (100 in binary), and 9 (1001 in binary). And 9 = a(0) + a(1) + a(2) + a(4) + a(9) = 0 + 1 + 1 + 2 + 5.

Crossrefs

Cf. A119709, A165416.

Sequence in context: A048620 A291271 A308318 * A117660 A358015 A184198

Adjacent sequences: A165416 A165417 A165418 * A165420 A165421 A165422

Keyword

base,nonn

Author

Leroy Quet, Sep 17 2009

Extensions

Extended by Ray Chandler, Mar 13 2010

Status

approved