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.
EXAMPLE
The terms together with their binary expansions and binary indices begin:
1: 1 ~ {1}
8: 1000 ~ {4}
9: 1001 ~ {1,4}
32: 100000 ~ {6}
33: 100001 ~ {1,6}
40: 101000 ~ {4,6}
41: 101001 ~ {1,4,6}
128: 10000000 ~ {8}
129: 10000001 ~ {1,8}
136: 10001000 ~ {4,8}
137: 10001001 ~ {1,4,8}
160: 10100000 ~ {6,8}
161: 10100001 ~ {1,6,8}
168: 10101000 ~ {4,6,8}
169: 10101001 ~ {1,4,6,8}
256: 100000000 ~ {9}
257: 100000001 ~ {1,9}
264: 100001000 ~ {4,9}
265: 100001001 ~ {1,4,9}
288: 100100000 ~ {6,9}
289: 100100001 ~ {1,6,9}
296: 100101000 ~ {4,6,9}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], And@@Not/@PrimeQ/@bpe[#]&]
CROSSREFS
For powers of 2 instead of nonprime numbers we have A253317.
For prime indices instead of binary indices we have A320628.
For prime instead of nonprime we have A326782.
For composite numbers we have A371444.
An opposite version is A371449.
A000961 lists prime-powers.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 30 2024
STATUS
approved