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

6, 12, 18, 20, 22, 24, 28, 30, 40, 48, 56, 66, 68, 70, 72, 76, 78, 80, 82, 84, 86, 88, 92, 94, 96, 104, 108, 110, 112, 114, 116, 118, 120, 124, 126, 132, 144, 148, 156, 160, 172, 176, 180, 188, 192, 196, 204, 208, 212, 220, 224, 236, 240, 244, 252, 258, 264

Offset

1,1

Comments

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.

Circularity means the last part is followed by the first.

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.

Links

Table of n, a(n) for n=1..57.

Example

The sequence of terms together with their binary expansions and binary indices begins:
    6:       110 ~ {2,3}
   12:      1100 ~ {3,4}
   18:     10010 ~ {2,5}
   20:     10100 ~ {3,5}
   22:     10110 ~ {2,3,5}
   24:     11000 ~ {4,5}
   28:     11100 ~ {3,4,5}
   30:     11110 ~ {2,3,4,5}
   40:    101000 ~ {4,6}
   48:    110000 ~ {5,6}
   56:    111000 ~ {4,5,6}
   66:   1000010 ~ {2,7}
   68:   1000100 ~ {3,7}
   70:   1000110 ~ {2,3,7}
   72:   1001000 ~ {4,7}
   76:   1001100 ~ {3,4,7}
   78:   1001110 ~ {2,3,4,7}
   80:   1010000 ~ {5,7}
   82:   1010010 ~ {2,5,7}
   84:   1010100 ~ {3,5,7}

Mathematica

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

Crossrefs

The composition version is A328599.

The necklace composition version is A328601.

Compositions with no consecutive divisors or multiples are A328508.

Numbers whose binary indices are pairwise indivisible are A326704.

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

Sequence in context: A049094 A105935 A105289 * A328671 A051774 A119357

Adjacent sequences: A328605 A328606 A328607 * A328609 A328610 A328611

Keyword

nonn

Author

Gus Wiseman, Oct 25 2019

Status

approved