A367911 - OEIS

%I #6 Dec 17 2023 11:23:37

%S 1,4,7,20,68,320,352,1088,3136,5184,13376,16704,17472,70720,82240,

%T 83008,90112,90176

%N Sorted positions of first appearances in A367905.

%C A binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, 18 has reversed binary expansion (0,1,0,0,1) and binary indices {2,5}.

%e The terms together with the corresponding set-systems begin:

%e       1: {{1}}

%e       4: {{1,2}}

%e       7: {{1},{2},{1,2}}

%e      20: {{1,2},{1,3}}

%e      68: {{1,2},{1,2,3}}

%e     320: {{1,2,3},{1,4}}

%e     352: {{2,3},{1,2,3},{1,4}}

%e    1088: {{1,2,3},{1,2,4}}

%e    3136: {{1,2,3},{1,2,4},{3,4}}

%e    5184: {{1,2,3},{1,2,4},{1,3,4}}

%e   13376: {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

%e   16704: {{1,2,3},{1,4},{1,2,3,4}}

%e   17472: {{1,2,3},{1,2,4},{1,2,3,4}}

%e   70720: {{1,2,3},{1,2,4},{1,3,4},{1,5}}

%e   82240: {{1,2,3},{1,4},{1,2,3,4},{1,5}}

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

%t c=Table[Length[Select[Tuples[bpe/@bpe[n]],UnsameQ@@#&]],{n,1000}];

%t Select[Range[Length[c]],FreeQ[Take[c,#-1],c[[#]]]&]

%Y Sorted positions of first appearances in A367905.

%Y The unsorted version is A367910.

%Y Multisets without distinctness are A367915, unsorted A367913.

%Y Without distinctness we have A368112, unsorted A368111.

%Y For sets instead of sequences we have A368185, unsorted A368184.

%Y A048793 lists binary indices, length A000120, sum A029931.

%Y A058891 counts set-systems, covering A003465, connected A323818.

%Y A070939 gives length of binary expansion.

%Y A096111 gives product of binary indices.

%Y Cf. A072639, A309326, A326031, A326702, A326753, A367902, A367906, A367907, A367912, A368109, A368183.

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Dec 16 2023