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A335237
Numbers whose binary indices are not a singleton nor pairwise coprime.
7
0, 10, 11, 14, 15, 26, 27, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 74, 75, 78, 79, 90, 91, 94, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 114, 115, 116
OFFSET
1,2
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.
FORMULA
Complement in A001477 of A326675 and A000079.
EXAMPLE
The sequence of terms together with their binary expansions and binary indices begins:
0: 0 ~ {}
10: 1010 ~ {2,4}
11: 1011 ~ {1,2,4}
14: 1110 ~ {2,3,4}
15: 1111 ~ {1,2,3,4}
26: 11010 ~ {2,4,5}
27: 11011 ~ {1,2,4,5}
30: 11110 ~ {2,3,4,5}
31: 11111 ~ {1,2,3,4,5}
34: 100010 ~ {2,6}
35: 100011 ~ {1,2,6}
36: 100100 ~ {3,6}
37: 100101 ~ {1,3,6}
38: 100110 ~ {2,3,6}
39: 100111 ~ {1,2,3,6}
40: 101000 ~ {4,6}
41: 101001 ~ {1,4,6}
42: 101010 ~ {2,4,6}
43: 101011 ~ {1,2,4,6}
44: 101100 ~ {3,4,6}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], !(Length[bpe[#]]==1||CoprimeQ@@bpe[#])&]
CROSSREFS
The version for prime indices is A316438.
The version for standard compositions is A335236.
Numbers whose binary indices are pairwise coprime or a singleton: A087087.
Non-coprime partitions are counted by A335240.
All of the following pertain to compositions in standard order (A066099):
- Length is A000120.
- Sum is A070939.
- Product is A124758.
- Reverse is A228351
- GCD is A326674.
- Heinz number is A333219.
- LCM is A333226.
Sequence in context: A373633 A373665 A373646 * A214864 A062844 A144980
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 28 2020
STATUS
approved