cp's OEIS Frontend

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

%I A335237 #7 May 30 2020 09:18:55
%S A335237 0,10,11,14,15,26,27,30,31,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
%T A335237 50,51,52,53,54,55,56,57,58,59,60,61,62,63,74,75,78,79,90,91,94,95,98,
%U A335237 99,100,101,102,103,104,105,106,107,108,109,110,111,114,115,116
%N A335237 Numbers whose binary indices are not a singleton nor pairwise coprime.
%C A335237 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 A335237 Complement in A001477 of A326675 and A000079.
%e A335237 The sequence of terms together with their binary expansions and binary indices begins:
%e A335237     0:       0 ~ {}
%e A335237    10:    1010 ~ {2,4}
%e A335237    11:    1011 ~ {1,2,4}
%e A335237    14:    1110 ~ {2,3,4}
%e A335237    15:    1111 ~ {1,2,3,4}
%e A335237    26:   11010 ~ {2,4,5}
%e A335237    27:   11011 ~ {1,2,4,5}
%e A335237    30:   11110 ~ {2,3,4,5}
%e A335237    31:   11111 ~ {1,2,3,4,5}
%e A335237    34:  100010 ~ {2,6}
%e A335237    35:  100011 ~ {1,2,6}
%e A335237    36:  100100 ~ {3,6}
%e A335237    37:  100101 ~ {1,3,6}
%e A335237    38:  100110 ~ {2,3,6}
%e A335237    39:  100111 ~ {1,2,3,6}
%e A335237    40:  101000 ~ {4,6}
%e A335237    41:  101001 ~ {1,4,6}
%e A335237    42:  101010 ~ {2,4,6}
%e A335237    43:  101011 ~ {1,2,4,6}
%e A335237    44:  101100 ~ {3,4,6}
%t A335237 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A335237 Select[Range[0,100],!(Length[bpe[#]]==1||CoprimeQ@@bpe[#])&]
%Y A335237 The version for prime indices is A316438.
%Y A335237 The version for standard compositions is A335236.
%Y A335237 Numbers whose binary indices are pairwise coprime or a singleton: A087087.
%Y A335237 Non-coprime partitions are counted by A335240.
%Y A335237 All of the following pertain to compositions in standard order (A066099):
%Y A335237 - Length is A000120.
%Y A335237 - Sum is A070939.
%Y A335237 - Product is A124758.
%Y A335237 - Reverse is A228351
%Y A335237 - GCD is A326674.
%Y A335237 - Heinz number is A333219.
%Y A335237 - LCM is A333226.
%Y A335237 Cf. A007360, A048793, A051424, A101268, A291166, A302569, A326675, A333227, A333228, A335235, A335239.
%K A335237 nonn
%O A335237 1,2
%A A335237 _Gus Wiseman_, May 28 2020