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

Author

Leroy Quet, Sep 17 2009

Keywords

• base
• nonn

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.

Examples

			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.

Extensions

Extended by Ray Chandler, Mar 13 2010