|
|
A368533
|
|
Numbers whose binary indices are all squarefree.
|
|
8
|
|
|
0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 51, 52, 53, 54, 55, 64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 82, 83, 84, 85, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 112, 113, 114, 115, 116, 117, 118, 119, 512
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
The complement first differs from A115419 in having 128.
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
|
|
|
EXAMPLE
|
The terms together with their binary expansions and binary indices begin:
0: 0 ~ {}
1: 1 ~ {1}
2: 10 ~ {2}
3: 11 ~ {1,2}
4: 100 ~ {3}
5: 101 ~ {1,3}
6: 110 ~ {2,3}
7: 111 ~ {1,2,3}
16: 10000 ~ {5}
17: 10001 ~ {1,5}
18: 10010 ~ {2,5}
19: 10011 ~ {1,2,5}
20: 10100 ~ {3,5}
21: 10101 ~ {1,3,5}
22: 10110 ~ {2,3,5}
23: 10111 ~ {1,2,3,5}
32: 100000 ~ {6}
33: 100001 ~ {1,6}
34: 100010 ~ {2,6}
35: 100011 ~ {1,2,6}
36: 100100 ~ {3,6}
37: 100101 ~ {1,3,6}
38: 100110 ~ {2,3,6}
|
|
MATHEMATICA
|
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], And@@SquareFreeQ/@bpe[#]&]
|
|
CROSSREFS
|
For prime indices instead of binary indices we have A302478.
The case of prime binary indices is A326782.
The case of squarefree product is A371289.
For prime-power product we have A371290.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|