cp's OEIS Frontend

A367915 Sorted positions of first appearances in A367912 (number of multisets that can be obtained by choosing a binary index of each binary index).

%I A367915 #7 Dec 17 2023 11:23:28
%S A367915 1,4,20,52,64,68,84,116,308,320,324,340,372,816,832,836,848,852,880,
%T A367915 884,1104,1108,1136,1360,1364,1392,1396,1904,1908,2868,2884,2900,2932,
%U A367915 3152,3184,3188,3412,3424,3440,3444,3952,3956,5188,5204,5216,5220,5236,5476
%N A367915 Sorted positions of first appearances in A367912 (number of multisets that can be obtained by choosing a binary index of each binary index).
%C A367915 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 A367915 The terms together with the corresponding set-systems begin:
%e A367915      1: {{1}}
%e A367915      4: {{1,2}}
%e A367915     20: {{1,2},{1,3}}
%e A367915     52: {{1,2},{1,3},{2,3}}
%e A367915     64: {{1,2,3}}
%e A367915     68: {{1,2},{1,2,3}}
%e A367915     84: {{1,2},{1,3},{1,2,3}}
%e A367915    116: {{1,2},{1,3},{2,3},{1,2,3}}
%e A367915    308: {{1,2},{1,3},{2,3},{1,4}}
%e A367915    320: {{1,2,3},{1,4}}
%e A367915    324: {{1,2},{1,2,3},{1,4}}
%e A367915    340: {{1,2},{1,3},{1,2,3},{1,4}}
%e A367915    372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}
%t A367915 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A367915 c=Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]],{n,10000}];
%t A367915 Select[Range[Length[c]],FreeQ[Take[c,#-1],c[[#]]]&]
%Y A367915 A version for multisets and divisors is A355734.
%Y A367915 Sorted positions of first appearances in A367912, for sequences A368109.
%Y A367915 The unsorted version is A367913.
%Y A367915 A048793 lists binary indices, length A000120, sum A029931.
%Y A367915 A058891 counts set-systems, covering A003465, connected A323818.
%Y A367915 A070939 gives length of binary expansion.
%Y A367915 A096111 gives product of binary indices.
%Y A367915 Cf. A072639, A309326, A326031, A326702, A326749, A326753, A355733, A355744, A367905, A367906, A367911, A368112, A368185.
%K A367915 nonn
%O A367915 1,2
%A A367915 _Gus Wiseman_, Dec 16 2023