A141299 a(n) = number (with repetition) of (not necessarily distinct) substrings in the binary representation of n that each occur multiple times.

0, 0, 2, 2, 2, 2, 5, 5, 4, 6, 3, 4, 3, 5, 9, 9, 7, 7, 5, 7, 11, 7, 6, 7, 5, 7, 6, 7, 6, 9, 14, 14, 11, 10, 8, 12, 10, 8, 8, 10, 10, 17, 12, 8, 12, 10, 10, 11, 8, 8, 8, 8, 12, 12, 8, 10, 8, 10, 8, 11, 10, 14, 20, 20, 16, 14, 12, 14, 13, 11, 11, 14, 19, 14, 11, 13, 11, 11, 12, 14, 13, 14, 11

Offset: 1

Author

Leroy Quet, Jun 24 2008

Keywords

• nonn

Comments

Substrings may start with a 0.

Examples

			0,0,1,1,10,10 each occur multiple times in binary 1010 = decimal 10. So a(10) = 6.
		

Links

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

Crossrefs

Cf. A141297, A141298, A141300.

Programs

Mathematica

Array[Function[d, Total@ Select[Tally@ Apply[Join, Map[Partition[d, #, 1] &, Range[Length@ d - 1]]], Last@ # > 1 &][[All, -1]]]@ IntegerDigits[#, 2] &, 83] (* Michael De Vlieger, Oct 23 2017 *)

Extensions

Extended by Ray Chandler, Jun 25 2009