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

Author

Leroy Quet, Jun 24 2008

Keywords

• nonn

Comments

Substrings may start with a 0.

Examples

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

Links

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

Crossrefs

Cf. A141297, A141299, A141300.

Programs

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 *)

Extensions

Extended by Ray Chandler, Jun 25 2009