A328608 - OEIS

%I #7 Oct 26 2019 10:00:30

%S 6,12,18,20,22,24,28,30,40,48,56,66,68,70,72,76,78,80,82,84,86,88,92,

%T 94,96,104,108,110,112,114,116,118,120,124,126,132,144,148,156,160,

%U 172,176,180,188,192,196,204,208,212,220,224,236,240,244,252,258,264

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

%C 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 Circularity means the last part is followed by the first.

%C 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 The sequence of terms together with their binary expansions and binary indices begins:

%e     6:       110 ~ {2,3}

%e    12:      1100 ~ {3,4}

%e    18:     10010 ~ {2,5}

%e    20:     10100 ~ {3,5}

%e    22:     10110 ~ {2,3,5}

%e    24:     11000 ~ {4,5}

%e    28:     11100 ~ {3,4,5}

%e    30:     11110 ~ {2,3,4,5}

%e    40:    101000 ~ {4,6}

%e    48:    110000 ~ {5,6}

%e    56:    111000 ~ {4,5,6}

%e    66:   1000010 ~ {2,7}

%e    68:   1000100 ~ {3,7}

%e    70:   1000110 ~ {2,3,7}

%e    72:   1001000 ~ {4,7}

%e    76:   1001100 ~ {3,4,7}

%e    78:   1001110 ~ {2,3,4,7}

%e    80:   1010000 ~ {5,7}

%e    82:   1010010 ~ {2,5,7}

%e    84:   1010100 ~ {3,5,7}

%t Select[Range[100],!MatchQ[Append[Join@@Position[Reverse[IntegerDigits[#,2]],1],1+IntegerExponent[#,2]],{___,x_,y_,___}/;Divisible[x,y]||Divisible[y,x]]&]

%Y The composition version is A328599.

%Y The necklace composition version is A328601.

%Y Compositions with no consecutive divisors or multiples are A328508.

%Y Numbers whose binary indices are pairwise indivisible are A326704.

%Y Cf. A000031, A318726, A318729, A328171, A328460, A328593, A328598, A328600, A328603.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 25 2019