A141298 a(n) = number of distinct substrings in the binary representation of n that each occur multiple times.

0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 1, 2, 1, 2, 3, 3, 3, 3, 2, 3, 5, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 4, 4, 4, 3, 5, 4, 3, 3, 4, 4, 7, 5, 3, 5, 4, 3, 4, 3, 3, 3, 3, 5, 5, 2, 4, 3, 4, 2, 4, 3, 4, 5, 5, 5, 5, 4, 5, 5, 4, 4, 5, 8, 5, 4, 5, 4, 4, 4, 5, 5, 5, 4, 7, 9, 5, 6, 4, 4, 5, 8, 4, 6, 5, 4, 5, 4, 4, 4, 5, 4, 5, 3, 4, 4

Offset

1,7

Comments

Substrings may start with a 0.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

The distinct substrings that occur multiple times in decimal 10 = binary 1010 are 0,1 and 10. So a(10)=3.

Mathematica

Table[With[{d = IntegerDigits[n, 2]}, Count[Split@ Sort@ Apply[Join, Table[Partition[d, k, 1], {k, Length@ d}]], _?(Length@ # > 1 &)]], {n, 105}] (* Michael De Vlieger, Sep 22 2017 *)

Crossrefs

Cf. A141297, A141299, A141300.

Sequence in context: A264025 A139465 A010244 * A256915 A348367 A209254

Adjacent sequences: A141295 A141296 A141297 * A141299 A141300 A141301

Keyword

nonn

Author

Leroy Quet, Jun 24 2008

Extensions

Extended by Ray Chandler, Jun 25 2009

Status

approved