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.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
Note that a number's binary and prime indices cannot have the same minimum; see A372437.
EXAMPLE
The binary indices of 345 are {1,4,5,7,9}, and the prime indices are {2,3,9}. Both have maximum 9, so 345 is in the sequence.
The terms together with their prime indices begin:
3: {2}
5: {3}
14: {1,4}
22: {1,5}
39: {2,6}
52: {1,1,6}
68: {1,1,7}
85: {3,7}
102: {1,2,7}
119: {4,7}
133: {4,8}
152: {1,1,1,8}
171: {2,2,8}
The terms together with their binary expansions and binary indices begin:
3: 11 ~ {1,2}
5: 101 ~ {1,3}
14: 1110 ~ {2,3,4}
22: 10110 ~ {2,3,5}
39: 100111 ~ {1,2,3,6}
52: 110100 ~ {3,5,6}
68: 1000100 ~ {3,7}
85: 1010101 ~ {1,3,5,7}
102: 1100110 ~ {2,3,6,7}
119: 1110111 ~ {1,2,3,5,6,7}
133: 10000101 ~ {1,3,8}
152: 10011000 ~ {4,5,8}
171: 10101011 ~ {1,2,4,6,8}
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], Max[prix[#]]==Max[bix[#]]&]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, May 04 2024
STATUS
approved