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

1,2

Comments

Substrings may start with a 0.

Links

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

Example

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

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 *)

Crossrefs

Cf. A141297, A141298, A141299.

Sequence in context: A125608 A182001 A099813 * A260502 A014388 A186693

Adjacent sequences: A141297 A141298 A141299 * A141301 A141302 A141303

Keyword

nonn

Author

Leroy Quet, Jun 24 2008

Extensions

Extended by Ray Chandler, Jun 25 2009

Status

approved