cp's OEIS Frontend

A368111 Least k such that there are exactly A003586(n) ways to choose a binary index of each binary index of k.

%I A368111 #7 Dec 18 2023 08:28:50
%S A368111 1,4,64,20,68,52,1088,84,308,1092,116,5184,820,1108,372,5188,2868,
%T A368111 1140,13376,884,5204,17204,1396,13380,2932,5236,275520,19252,1908,
%U A368111 13396,17268,5492,275524,84788,3956,13428,1324096,19316,6004,275540,215860,18292,13684
%N A368111 Least k such that there are exactly A003586(n) ways to choose a binary index of each binary index of k.
%C A368111 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 A368111 The terms together with the corresponding set-systems begin:
%e A368111     1: {{1}}
%e A368111     4: {{1,2}}
%e A368111    64: {{1,2,3}}
%e A368111    20: {{1,2},{1,3}}
%e A368111    68: {{1,2},{1,2,3}}
%e A368111    52: {{1,2},{1,3},{2,3}}
%e A368111    84: {{1,2},{1,3},{1,2,3}}
%e A368111   308: {{1,2},{1,3},{2,3},{1,4}}
%e A368111   116: {{1,2},{1,3},{2,3},{1,2,3}}
%e A368111   820: {{1,2},{1,3},{2,3},{1,4},{2,4}}
%e A368111   372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}
%e A368111   884: {{1,2},{1,3},{2,3},{1,2,3},{1,4},{2,4}}
%t A368111 nn=10000;
%t A368111 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A368111 dd=Select[Range[nn],Max@@First/@FactorInteger[#]<=3&];
%t A368111 qq=Table[Length[Tuples[bpe/@bpe[n]]],{n,nn}];
%t A368111 kk=Select[Range[Length[dd]],SubsetQ[qq,Take[dd,#]]&]
%t A368111 Table[Position[qq,dd[[n]]][[1,1]],{n,kk}]
%Y A368111 With distinctness we have A367910, sorted A367911, firsts of A367905.
%Y A368111 For multisets we have A367913, sorted A367915, firsts of A367912.
%Y A368111 Positions of first appearances in A368109.
%Y A368111 The sorted version is A368112.
%Y A368111 A048793 lists binary indices, length A000120, sum A029931.
%Y A368111 A058891 counts set-systems, covering A003465, connected A323818.
%Y A368111 A070939 gives length of binary expansion.
%Y A368111 A096111 gives product of binary indices.
%Y A368111 Cf. A072639, A253317, A309326, A326031, A326702, A326753, A355731, A355741, A355744, A367906.
%K A368111 nonn
%O A368111 1,2
%A A368111 _Gus Wiseman_, Dec 17 2023