A367915 - OEIS

%I #7 Dec 17 2023 11:23:28

%S 1,4,20,52,64,68,84,116,308,320,324,340,372,816,832,836,848,852,880,

%T 884,1104,1108,1136,1360,1364,1392,1396,1904,1908,2868,2884,2900,2932,

%U 3152,3184,3188,3412,3424,3440,3444,3952,3956,5188,5204,5216,5220,5236,5476

%N Sorted positions of first appearances in A367912 (number of multisets that can be obtained by choosing a binary index of each binary index).

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

%e     52: {{1,2},{1,3},{2,3}}

%e     64: {{1,2,3}}

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

%e     84: {{1,2},{1,3},{1,2,3}}

%e    116: {{1,2},{1,3},{2,3},{1,2,3}}

%e    308: {{1,2},{1,3},{2,3},{1,4}}

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

%e    324: {{1,2},{1,2,3},{1,4}}

%e    340: {{1,2},{1,3},{1,2,3},{1,4}}

%e    372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}

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

%t c=Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]],{n,10000}];

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

%Y A version for multisets and divisors is A355734.

%Y Sorted positions of first appearances in A367912, for sequences A368109.

%Y The unsorted version is A367913.

%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, A326749, A326753, A355733, A355744, A367905, A367906, A367911, A368112, A368185.

%K nonn

%O 1,2

%A _Gus Wiseman_, Dec 16 2023