cp's OEIS Frontend

A328608 Numbers whose binary indices have no part circularly followed by a divisor or a multiple.

%I A328608 #7 Oct 26 2019 10:00:30
%S A328608 6,12,18,20,22,24,28,30,40,48,56,66,68,70,72,76,78,80,82,84,86,88,92,
%T A328608 94,96,104,108,110,112,114,116,118,120,124,126,132,144,148,156,160,
%U A328608 172,176,180,188,192,196,204,208,212,220,224,236,240,244,252,258,264
%N A328608 Numbers whose binary indices have no part circularly followed by a divisor or a multiple.
%C A328608 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 A328608 Circularity means the last part is followed by the first.
%C A328608 Note that this is a somewhat degenerate case, as a part could only be followed by a divisor if it is the last part followed by the first.
%e A328608 The sequence of terms together with their binary expansions and binary indices begins:
%e A328608     6:       110 ~ {2,3}
%e A328608    12:      1100 ~ {3,4}
%e A328608    18:     10010 ~ {2,5}
%e A328608    20:     10100 ~ {3,5}
%e A328608    22:     10110 ~ {2,3,5}
%e A328608    24:     11000 ~ {4,5}
%e A328608    28:     11100 ~ {3,4,5}
%e A328608    30:     11110 ~ {2,3,4,5}
%e A328608    40:    101000 ~ {4,6}
%e A328608    48:    110000 ~ {5,6}
%e A328608    56:    111000 ~ {4,5,6}
%e A328608    66:   1000010 ~ {2,7}
%e A328608    68:   1000100 ~ {3,7}
%e A328608    70:   1000110 ~ {2,3,7}
%e A328608    72:   1001000 ~ {4,7}
%e A328608    76:   1001100 ~ {3,4,7}
%e A328608    78:   1001110 ~ {2,3,4,7}
%e A328608    80:   1010000 ~ {5,7}
%e A328608    82:   1010010 ~ {2,5,7}
%e A328608    84:   1010100 ~ {3,5,7}
%t A328608 Select[Range[100],!MatchQ[Append[Join@@Position[Reverse[IntegerDigits[#,2]],1],1+IntegerExponent[#,2]],{___,x_,y_,___}/;Divisible[x,y]||Divisible[y,x]]&]
%Y A328608 The composition version is A328599.
%Y A328608 The necklace composition version is A328601.
%Y A328608 Compositions with no consecutive divisors or multiples are A328508.
%Y A328608 Numbers whose binary indices are pairwise indivisible are A326704.
%Y A328608 Cf. A000031, A318726, A318729, A328171, A328460, A328593, A328598, A328600, A328603.
%K A328608 nonn
%O A328608 1,1
%A A328608 _Gus Wiseman_, Oct 25 2019