cp's OEIS Frontend

A328592 Numbers whose binary expansion has all different lengths of runs of 1's.

%I A328592 #9 Oct 25 2019 10:04:33
%S A328592 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,
%T A328592 35,38,39,44,46,47,48,49,50,52,55,56,57,58,59,60,61,62,63,64,67,70,71,
%U A328592 76,78,79,88,92,94,95,96,97,98,100,103,104,110,111,112,113,114
%N A328592 Numbers whose binary expansion has all different lengths of runs of 1's.
%C A328592 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.
%C A328592 The complement is {5, 9, 10, 17, 18, 20, 21, 27, ...}.
%e A328592 The sequence of terms together with their binary expansions and binary indices begins:
%e A328592    0:     0 ~ {}
%e A328592    1:     1 ~ {1}
%e A328592    2:    10 ~ {2}
%e A328592    3:    11 ~ {1,2}
%e A328592    4:   100 ~ {3}
%e A328592    6:   110 ~ {2,3}
%e A328592    7:   111 ~ {1,2,3}
%e A328592    8:  1000 ~ {4}
%e A328592   11:  1011 ~ {1,2,4}
%e A328592   12:  1100 ~ {3,4}
%e A328592   13:  1101 ~ {1,3,4}
%e A328592   14:  1110 ~ {2,3,4}
%e A328592   15:  1111 ~ {1,2,3,4}
%e A328592   16: 10000 ~ {5}
%e A328592   19: 10011 ~ {1,2,5}
%e A328592   22: 10110 ~ {2,3,5}
%e A328592   23: 10111 ~ {1,2,3,5}
%e A328592   24: 11000 ~ {4,5}
%e A328592   25: 11001 ~ {1,4,5}
%e A328592   26: 11010 ~ {2,4,5}
%t A328592 Select[Range[0,100],UnsameQ@@Length/@Split[Join@@Position[Reverse[IntegerDigits[#,2]],1],#2==#1+1&]&]
%Y A328592 The version for prime indices is A130091.
%Y A328592 The binary expansion of n has A069010(n) runs of 1's.
%Y A328592 The lengths of runs of 1's in the binary expansion of n are row n of A245563.
%Y A328592 Numbers whose binary expansion has equal lengths of runs of 1's are A164707.
%Y A328592 Cf. A000120, A003714, A014081, A098859, A121016, A328593, A328595, A328596.
%K A328592 nonn
%O A328592 1,3
%A A328592 _Gus Wiseman_, Oct 20 2019