cp's OEIS Frontend

A328593 Numbers whose binary indices have no consecutive divisible parts.

%I A328593 #6 Oct 25 2019 10:04:41
%S A328593 0,1,2,4,6,8,12,14,16,18,20,22,24,28,30,32,40,44,46,48,50,52,54,56,60,
%T A328593 62,64,66,68,70,72,76,78,80,82,84,86,88,92,94,96,104,108,110,112,114,
%U A328593 116,118,120,124,126,128,132,134,144,146,148,150,152,156,158,160
%N A328593 Numbers whose binary indices have no consecutive divisible parts.
%C A328593 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.
%e A328593 The sequence of terms together with their binary expansions and binary indices begins:
%e A328593    0:      0 ~ {}
%e A328593    1:      1 ~ {1}
%e A328593    2:     10 ~ {2}
%e A328593    4:    100 ~ {3}
%e A328593    6:    110 ~ {2,3}
%e A328593    8:   1000 ~ {4}
%e A328593   12:   1100 ~ {3,4}
%e A328593   14:   1110 ~ {2,3,4}
%e A328593   16:  10000 ~ {5}
%e A328593   18:  10010 ~ {2,5}
%e A328593   20:  10100 ~ {3,5}
%e A328593   22:  10110 ~ {2,3,5}
%e A328593   24:  11000 ~ {4,5}
%e A328593   28:  11100 ~ {3,4,5}
%e A328593   30:  11110 ~ {2,3,4,5}
%e A328593   32: 100000 ~ {6}
%e A328593   40: 101000 ~ {4,6}
%e A328593   44: 101100 ~ {3,4,6}
%e A328593   46: 101110 ~ {2,3,4,6}
%e A328593   48: 110000 ~ {5,6}
%e A328593   50: 110010 ~ {2,5,6}
%t A328593 Select[Range[0,100],!MatchQ[Join@@Position[Reverse[IntegerDigits[#,2]],1],{___,x_,y_,___}/;Divisible[y,x]]&]
%Y A328593 The version for prime indices is A328603.
%Y A328593 Numbers with no successive binary indices are A003714.
%Y A328593 Partitions with no consecutive divisible parts are A328171.
%Y A328593 Compositions without consecutive divisible parts are A328460.
%Y A328593 Cf. A000120, A014081, A328187, A328508, A328594, A328595, A328598, A328600, A328608.
%K A328593 nonn
%O A328593 1,3
%A A328593 _Gus Wiseman_, Oct 21 2019