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

1,3

Comments

Substrings may start with a 0.

Links

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

Example

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

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 *)

Crossrefs

Cf. A141297, A141298, A141300.

Sequence in context: A177333 A118486 A288026 * A035681 A195601 A352723

Adjacent sequences: A141296 A141297 A141298 * A141300 A141301 A141302

Keyword

nonn

Author

Leroy Quet, Jun 24 2008

Extensions

Extended by Ray Chandler, Jun 25 2009

Status

approved