OFFSET
1,1
COMMENTS
EXAMPLE
The binary indices of 18 are {2,5}, and the prime indices are {1,2,2}, so 18 is in the sequence.
The terms together with their prime indices begin:
3: {2}
5: {3}
6: {1,2}
14: {1,4}
15: {2,3}
18: {1,2,2}
20: {1,1,3}
22: {1,5}
27: {2,2,2}
28: {1,1,4}
30: {1,2,3}
The terms together with their binary expansions and binary indices begin:
3: 11 ~ {1,2}
5: 101 ~ {1,3}
6: 110 ~ {2,3}
14: 1110 ~ {2,3,4}
15: 1111 ~ {1,2,3,4}
18: 10010 ~ {2,5}
20: 10100 ~ {3,5}
22: 10110 ~ {2,3,5}
27: 11011 ~ {1,2,4,5}
28: 11100 ~ {3,4,5}
30: 11110 ~ {2,3,4,5}
MATHEMATICA
bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Intersection[bix[#], prix[#]]!={}&]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, May 03 2024
STATUS
approved