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 sequence of terms together with their binary expansions and binary indices begins:
1: 1 ~ {1}
6: 110 ~ {2,3}
12: 1100 ~ {3,4}
18: 10010 ~ {2,5}
20: 10100 ~ {3,5}
22: 10110 ~ {2,3,5}
24: 11000 ~ {4,5}
28: 11100 ~ {3,4,5}
48: 110000 ~ {5,6}
56: 111000 ~ {4,5,6}
66: 1000010 ~ {2,7}
68: 1000100 ~ {3,7}
70: 1000110 ~ {2,3,7}
72: 1001000 ~ {4,7}
76: 1001100 ~ {3,4,7}
80: 1010000 ~ {5,7}
82: 1010010 ~ {2,5,7}
84: 1010100 ~ {3,5,7}
86: 1010110 ~ {2,3,5,7}
88: 1011000 ~ {4,5,7}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Select[Range[100], GCD@@bpe[#]==1&&stableQ[bpe[#], Divisible]&]
CROSSREFS
The version for prime indices (instead of binary indices) is A328677.
Numbers whose binary indices are relatively prime are A291166.
Numbers whose distinct prime indices are pairwise indivisible are A316476.
BII-numbers of antichains are A326704.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 29 2019
STATUS
approved