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.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..1000
EXAMPLE
The sequence together with the corresponding binary expansions and binary indices begins:
1: 1 ~ {1}
2: 10 ~ {2}
4: 100 ~ {3}
8: 1000 ~ {4}
16: 10000 ~ {5}
6: 110 ~ {2,3}
64: 1000000 ~ {7}
128: 10000000 ~ {8}
256: 100000000 ~ {9}
18: 10010 ~ {2,5}
1024: 10000000000 ~ {11}
12: 1100 ~ {3,4}
4096: 1000000000000 ~ {13}
66: 1000010 ~ {2,7}
20: 10100 ~ {3,5}
32768: 1000000000000000 ~ {16}
65536: 10000000000000000 ~ {17}
258: 100000010 ~ {2,9}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
q=Table[LCM@@bpe[n], {n, 10000}];
Table[Position[q, i][[1, 1]], {i, First[Split[Union[q], #1+1==#2&]]}]
CROSSREFS
The version for prime indices is A330225.
The version for standard compositions is A333225.
Let q(k) be the binary indices of k:
- The sum of q(k) is A029931(k).
- The elements of q(k) are row k of A048793.
- The product of q(k) is A096111(k).
- The LCM of q(k) is A271410(k).
- The GCD of q(k) is A326674(k).
GCD of prime indices is A289508.
LCM of prime indices is A290103.
LCM of standard compositions is A333226.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2020
EXTENSIONS
Terms a(23) and beyond from Giovanni Resta, Mar 29 2020
STATUS
approved