OFFSET
1,1
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.
Do 2, 3, 4, 7, 12, 14 appear just once?
Are 1, 5, 9 missing?
The above questions hold true up to n = 10^6. - John Tyler Rascoe, May 21 2024
LINKS
John Tyler Rascoe, Table of n, a(n) for n = 1..9438
FORMULA
a(n) = A029931(prime(n)).
EXAMPLE
The primes together with their binary expansions and binary indices begin:
2: 10 ~ {2}
3: 11 ~ {1,2}
5: 101 ~ {1,3}
7: 111 ~ {1,2,3}
11: 1011 ~ {1,2,4}
13: 1101 ~ {1,3,4}
17: 10001 ~ {1,5}
19: 10011 ~ {1,2,5}
23: 10111 ~ {1,2,3,5}
29: 11101 ~ {1,3,4,5}
31: 11111 ~ {1,2,3,4,5}
37: 100101 ~ {1,3,6}
41: 101001 ~ {1,4,6}
43: 101011 ~ {1,2,4,6}
47: 101111 ~ {1,2,3,4,6}
53: 110101 ~ {1,3,5,6}
59: 111011 ~ {1,2,4,5,6}
61: 111101 ~ {1,3,4,5,6}
67: 1000011 ~ {1,2,7}
71: 1000111 ~ {1,2,3,7}
73: 1001001 ~ {1,4,7}
79: 1001111 ~ {1,2,3,4,7}
MATHEMATICA
bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Total[bix[Prime[n]]], {n, 100}]
CROSSREFS
The number instead of sum of binary indices is A014499.
Row-sums of A372471.
A056239 adds up prime indices.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A326031 gives weight of the set-system with BII-number n.
A372427 lists numbers whose binary and prime indices have the same sum.
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, May 02 2024
STATUS
approved