A335237 - OEIS

%I #7 May 30 2020 09:18:55

%S 0,10,11,14,15,26,27,30,31,34,35,36,37,38,39,40,41,42,43,44,45,46,47,

%T 50,51,52,53,54,55,56,57,58,59,60,61,62,63,74,75,78,79,90,91,94,95,98,

%U 99,100,101,102,103,104,105,106,107,108,109,110,111,114,115,116

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

%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.

%F Complement in A001477 of A326675 and A000079.

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

%e     0:       0 ~ {}

%e    10:    1010 ~ {2,4}

%e    11:    1011 ~ {1,2,4}

%e    14:    1110 ~ {2,3,4}

%e    15:    1111 ~ {1,2,3,4}

%e    26:   11010 ~ {2,4,5}

%e    27:   11011 ~ {1,2,4,5}

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

%e    31:   11111 ~ {1,2,3,4,5}

%e    34:  100010 ~ {2,6}

%e    35:  100011 ~ {1,2,6}

%e    36:  100100 ~ {3,6}

%e    37:  100101 ~ {1,3,6}

%e    38:  100110 ~ {2,3,6}

%e    39:  100111 ~ {1,2,3,6}

%e    40:  101000 ~ {4,6}

%e    41:  101001 ~ {1,4,6}

%e    42:  101010 ~ {2,4,6}

%e    43:  101011 ~ {1,2,4,6}

%e    44:  101100 ~ {3,4,6}

%t bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t Select[Range[0,100],!(Length[bpe[#]]==1||CoprimeQ@@bpe[#])&]

%Y The version for prime indices is A316438.

%Y The version for standard compositions is A335236.

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

%Y Non-coprime partitions are counted by A335240.

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

%Y - Length is A000120.

%Y - Sum is A070939.

%Y - Product is A124758.

%Y - Reverse is A228351

%Y - GCD is A326674.

%Y - Heinz number is A333219.

%Y - LCM is A333226.

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

%K nonn

%O 1,2

%A _Gus Wiseman_, May 28 2020