A328593 Numbers whose binary indices have no consecutive divisible parts.

0, 1, 2, 4, 6, 8, 12, 14, 16, 18, 20, 22, 24, 28, 30, 32, 40, 44, 46, 48, 50, 52, 54, 56, 60, 62, 64, 66, 68, 70, 72, 76, 78, 80, 82, 84, 86, 88, 92, 94, 96, 104, 108, 110, 112, 114, 116, 118, 120, 124, 126, 128, 132, 134, 144, 146, 148, 150, 152, 156, 158, 160

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..62.

Example

The sequence of terms together with their binary expansions and binary indices begins:
   0:      0 ~ {}
   1:      1 ~ {1}
   2:     10 ~ {2}
   4:    100 ~ {3}
   6:    110 ~ {2,3}
   8:   1000 ~ {4}
  12:   1100 ~ {3,4}
  14:   1110 ~ {2,3,4}
  16:  10000 ~ {5}
  18:  10010 ~ {2,5}
  20:  10100 ~ {3,5}
  22:  10110 ~ {2,3,5}
  24:  11000 ~ {4,5}
  28:  11100 ~ {3,4,5}
  30:  11110 ~ {2,3,4,5}
  32: 100000 ~ {6}
  40: 101000 ~ {4,6}
  44: 101100 ~ {3,4,6}
  46: 101110 ~ {2,3,4,6}
  48: 110000 ~ {5,6}
  50: 110010 ~ {2,5,6}

Mathematica

Select[Range[0, 100], !MatchQ[Join@@Position[Reverse[IntegerDigits[#, 2]], 1], {___, x_, y_, ___}/; Divisible[y, x]]&]

Crossrefs

The version for prime indices is A328603.

Numbers with no successive binary indices are A003714.

Partitions with no consecutive divisible parts are A328171.

Compositions without consecutive divisible parts are A328460.

Cf. A000120, A014081, A328187, A328508, A328594, A328595, A328598, A328600, A328608.

Sequence in context: A103829 A164530 A058817 * A254748 A217562 A088879

Adjacent sequences: A328590 A328591 A328592 * A328594 A328595 A328596

Keyword

nonn

Author

Gus Wiseman, Oct 21 2019

Status

approved