A335237 Numbers whose binary indices are not a singleton nor pairwise coprime.

0, 10, 11, 14, 15, 26, 27, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 74, 75, 78, 79, 90, 91, 94, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 114, 115, 116

Offset

1,2

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.

Links

Table of n, a(n) for n=1..62.

Formula

Complement in A001477 of A326675 and A000079.

Example

The sequence of terms together with their binary expansions and binary indices begins:
    0:       0 ~ {}
   10:    1010 ~ {2,4}
   11:    1011 ~ {1,2,4}
   14:    1110 ~ {2,3,4}
   15:    1111 ~ {1,2,3,4}
   26:   11010 ~ {2,4,5}
   27:   11011 ~ {1,2,4,5}
   30:   11110 ~ {2,3,4,5}
   31:   11111 ~ {1,2,3,4,5}
   34:  100010 ~ {2,6}
   35:  100011 ~ {1,2,6}
   36:  100100 ~ {3,6}
   37:  100101 ~ {1,3,6}
   38:  100110 ~ {2,3,6}
   39:  100111 ~ {1,2,3,6}
   40:  101000 ~ {4,6}
   41:  101001 ~ {1,4,6}
   42:  101010 ~ {2,4,6}
   43:  101011 ~ {1,2,4,6}
   44:  101100 ~ {3,4,6}

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], !(Length[bpe[#]]==1||CoprimeQ@@bpe[#])&]

Crossrefs

The version for prime indices is A316438.

The version for standard compositions is A335236.

Numbers whose binary indices are pairwise coprime or a singleton: A087087.

Non-coprime partitions are counted by A335240.

All of the following pertain to compositions in standard order (A066099):

- Length is A000120.

- Sum is A070939.

- Product is A124758.

- Reverse is A228351

- GCD is A326674.

- Heinz number is A333219.

- LCM is A333226.

Cf. A007360, A048793, A051424, A101268, A291166, A302569, A326675, A333227, A333228, A335235, A335239.

Sequence in context: A085186 A345289 A298365 * A214864 A062844 A144980

Adjacent sequences: A335234 A335235 A335236 * A335238 A335239 A335240

Keyword

nonn

Author

Gus Wiseman, May 28 2020

Status

approved