A141300 a(n) = number of distinct (nonempty) substrings in the binary representation of n that each occur exactly once.

1, 3, 1, 4, 4, 4, 1, 5, 6, 4, 7, 6, 7, 5, 1, 6, 8, 8, 10, 8, 4, 8, 9, 8, 10, 8, 9, 8, 9, 6, 1, 7, 10, 11, 13, 9, 11, 13, 13, 11, 11, 4, 9, 13, 9, 11, 11, 10, 13, 13, 13, 13, 9, 9, 13, 11, 13, 11, 13, 10, 11, 7, 1, 8, 12, 14, 16, 14, 15, 17, 17, 14, 9, 14, 17, 15, 17, 17, 16, 14, 15, 14, 17

Offset: 1

Author

Leroy Quet, Jun 24 2008

Keywords

• nonn

Comments

Substrings may start with a 0.

Examples

			In (decimal 10 =) binary 1010: 01, 101, 010, 1010 each occur exactly once. So a(10) = 4.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A141297, A141298, A141299.

Programs

Mathematica

Array[Function[d, Count[Tally@ Apply[Join, Map[Partition[d, #, 1] &, Range[Length@ d]]], ?(Last@ # == 1 &)]]@ IntegerDigits[#, 2] &, 83] (* _Michael De Vlieger, Oct 23 2017 *)

Extensions

Extended by Ray Chandler, Jun 25 2009