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A328593
Numbers whose binary indices have no consecutive divisible parts.
10
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.
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.
Sequence in context: A103829 A164530 A058817 * A254748 A217562 A088879
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 21 2019
STATUS
approved