OFFSET
1,1
COMMENTS
EXAMPLE
The binary indices of 89 are {1,4,5,7}, with sum 17, which is prime, so 89 is in the sequence.
The terms together with their binary expansions and binary indices begin:
2: 10 ~ {2}
3: 11 ~ {1,2}
11: 1011 ~ {1,2,4}
23: 10111 ~ {1,2,3,5}
29: 11101 ~ {1,3,4,5}
41: 101001 ~ {1,4,6}
43: 101011 ~ {1,2,4,6}
61: 111101 ~ {1,3,4,5,6}
71: 1000111 ~ {1,2,3,7}
79: 1001111 ~ {1,2,3,4,7}
89: 1011001 ~ {1,4,5,7}
101: 1100101 ~ {1,3,6,7}
103: 1100111 ~ {1,2,3,6,7}
113: 1110001 ~ {1,5,6,7}
131: 10000011 ~ {1,2,8}
137: 10001001 ~ {1,4,8}
149: 10010101 ~ {1,3,5,8}
151: 10010111 ~ {1,2,3,5,8}
163: 10100011 ~ {1,2,6,8}
181: 10110101 ~ {1,3,5,6,8}
191: 10111111 ~ {1,2,3,4,5,6,8}
197: 11000101 ~ {1,3,7,8}
MATHEMATICA
Select[Range[100], PrimeQ[#] && PrimeQ[Total[First/@Position[Reverse[IntegerDigits[#, 2]], 1]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2024
STATUS
approved