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A328592
Numbers whose binary expansion has all different lengths of runs of 1's.
24
0, 1, 2, 3, 4, 6, 7, 8, 11, 12, 13, 14, 15, 16, 19, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 35, 38, 39, 44, 46, 47, 48, 49, 50, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 70, 71, 76, 78, 79, 88, 92, 94, 95, 96, 97, 98, 100, 103, 104, 110, 111, 112, 113, 114
OFFSET
1,3
COMMENTS
Also numbers whose binary indices have different lengths of runs of successive parts. 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.
The complement is {5, 9, 10, 17, 18, 20, 21, 27, ...}.
EXAMPLE
The sequence of terms together with their binary expansions and binary indices begins:
0: 0 ~ {}
1: 1 ~ {1}
2: 10 ~ {2}
3: 11 ~ {1,2}
4: 100 ~ {3}
6: 110 ~ {2,3}
7: 111 ~ {1,2,3}
8: 1000 ~ {4}
11: 1011 ~ {1,2,4}
12: 1100 ~ {3,4}
13: 1101 ~ {1,3,4}
14: 1110 ~ {2,3,4}
15: 1111 ~ {1,2,3,4}
16: 10000 ~ {5}
19: 10011 ~ {1,2,5}
22: 10110 ~ {2,3,5}
23: 10111 ~ {1,2,3,5}
24: 11000 ~ {4,5}
25: 11001 ~ {1,4,5}
26: 11010 ~ {2,4,5}
MATHEMATICA
Select[Range[0, 100], UnsameQ@@Length/@Split[Join@@Position[Reverse[IntegerDigits[#, 2]], 1], #2==#1+1&]&]
CROSSREFS
The version for prime indices is A130091.
The binary expansion of n has A069010(n) runs of 1's.
The lengths of runs of 1's in the binary expansion of n are row n of A245563.
Numbers whose binary expansion has equal lengths of runs of 1's are A164707.
Sequence in context: A093452 A082103 A219618 * A175413 A192048 A235035
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 20 2019
STATUS
approved