OFFSET
1,1
COMMENTS
EXAMPLE
The binary indices of 60 are {3,4,5,6}, the prime indices are {1,1,2,3}, and 3 = 3, so 60 is in the sequence.
The terms together with their prime indices begin:
6: {1,2}
18: {1,2,2}
20: {1,1,3}
54: {1,2,2,2}
56: {1,1,1,4}
60: {1,1,2,3}
100: {1,1,3,3}
162: {1,2,2,2,2}
168: {1,1,1,2,4}
176: {1,1,1,1,5}
180: {1,1,2,2,3}
280: {1,1,1,3,4}
300: {1,1,2,3,3}
The terms together with their binary expansions and binary indices begin:
6: 110 ~ {2,3}
18: 10010 ~ {2,5}
20: 10100 ~ {3,5}
54: 110110 ~ {2,3,5,6}
56: 111000 ~ {4,5,6}
60: 111100 ~ {3,4,5,6}
100: 1100100 ~ {3,6,7}
162: 10100010 ~ {2,6,8}
168: 10101000 ~ {4,6,8}
176: 10110000 ~ {5,6,8}
180: 10110100 ~ {3,5,6,8}
280: 100011000 ~ {4,5,9}
300: 100101100 ~ {3,4,6,9}
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[1000], Min[bix[#]]==Max[prix[#]]&]
CROSSREFS
A070939 gives length of binary expansion.
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, May 04 2024
STATUS
approved