A328592 Numbers whose binary expansion has all different lengths of runs of 1's.

0, 1, 2, 3, 4, 6, 7, 8, 11, 12, 13, 14, 15, 16, 19, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 35, 38, 39, 44, 46, 47, 48, 49, 50, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 70, 71, 76, 78, 79, 88, 92, 94, 95, 96, 97, 98, 100, 103, 104, 110, 111, 112, 113, 114

Offset

1,3

Comments

Also numbers whose binary indices have different lengths of runs of successive parts. A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

The complement is {5, 9, 10, 17, 18, 20, 21, 27, ...}.

Links

Table of n, a(n) for n=1..66.

Example

The sequence of terms together with their binary expansions and binary indices begins:
   0:     0 ~ {}
   1:     1 ~ {1}
   2:    10 ~ {2}
   3:    11 ~ {1,2}
   4:   100 ~ {3}
   6:   110 ~ {2,3}
   7:   111 ~ {1,2,3}
   8:  1000 ~ {4}
  11:  1011 ~ {1,2,4}
  12:  1100 ~ {3,4}
  13:  1101 ~ {1,3,4}
  14:  1110 ~ {2,3,4}
  15:  1111 ~ {1,2,3,4}
  16: 10000 ~ {5}
  19: 10011 ~ {1,2,5}
  22: 10110 ~ {2,3,5}
  23: 10111 ~ {1,2,3,5}
  24: 11000 ~ {4,5}
  25: 11001 ~ {1,4,5}
  26: 11010 ~ {2,4,5}

Mathematica

Select[Range[0, 100], UnsameQ@@Length/@Split[Join@@Position[Reverse[IntegerDigits[#, 2]], 1], #2==#1+1&]&]

Crossrefs

The version for prime indices is A130091.

The binary expansion of n has A069010(n) runs of 1's.

The lengths of runs of 1's in the binary expansion of n are row n of A245563.

Numbers whose binary expansion has equal lengths of runs of 1's are A164707.

Cf. A000120, A003714, A014081, A098859, A121016, A328593, A328595, A328596.

Sequence in context: A093452 A082103 A219618 * A175413 A192048 A235035

Adjacent sequences: A328589 A328590 A328591 * A328593 A328594 A328595

Keyword

nonn

Author

Gus Wiseman, Oct 20 2019

Status

approved