cp's OEIS Frontend

A367913 Least number k such that there are exactly n ways to choose a multiset consisting of a binary index of each binary index of k.

%I A367913 #6 Dec 17 2023 11:23:32
%S A367913 1,4,64,20,68,320,52,84,16448,324,832,116,1104,308,816,340,836,848,
%T A367913 1108,1136,1360,3152,16708,372,5188,5216,852,880,2884,1364,13376,1392,
%U A367913 3184,3424,17220,5204,5220,2868,5728,884,19536,66896,2900,1396,21572,3188,3412
%N A367913 Least number k such that there are exactly n ways to choose a multiset consisting of a binary index of each binary index of k.
%C A367913 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 A367913 The terms together with the corresponding set-systems begin:
%e A367913       1: {{1}}
%e A367913       4: {{1,2}}
%e A367913      64: {{1,2,3}}
%e A367913      20: {{1,2},{1,3}}
%e A367913      68: {{1,2},{1,2,3}}
%e A367913     320: {{1,2,3},{1,4}}
%e A367913      52: {{1,2},{1,3},{2,3}}
%e A367913      84: {{1,2},{1,3},{1,2,3}}
%e A367913   16448: {{1,2,3},{1,2,3,4}}
%e A367913     324: {{1,2},{1,2,3},{1,4}}
%e A367913     832: {{1,2,3},{1,4},{2,4}}
%e A367913     116: {{1,2},{1,3},{2,3},{1,2,3}}
%t A367913 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A367913 spnm[y_]:=Max@@NestWhile[Most,y,Union[#]!=Range[0,Max@@#]&];
%t A367913 c=Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]],{n,1000}];
%t A367913 Table[Position[c,n][[1,1]],{n,spnm[c]}]
%Y A367913 A version for multisets and divisors is A355734.
%Y A367913 With distinctness we have A367910, firsts of A367905, sorted A367911.
%Y A367913 Positions of first appearances in A367912.
%Y A367913 The sorted version is A367915.
%Y A367913 For sequences we have A368111, firsts of A368109, sorted A368112.
%Y A367913 For sets we have A368184, firsts of A368183, sorted A368185.
%Y A367913 A048793 lists binary indices, length A000120, sum A029931.
%Y A367913 A058891 counts set-systems, covering A003465, connected A323818.
%Y A367913 A070939 gives length of binary expansion.
%Y A367913 A096111 gives product of binary indices.
%Y A367913 Cf. A072639, A309326, A326031, A326702, A326749, A326753, A355733, A355741, A355744.
%K A367913 nonn
%O A367913 1,2
%A A367913 _Gus Wiseman_, Dec 16 2023