cp's OEIS Frontend

A368112 Sorted positions of first appearances in A368109 (number of ways to choose a binary index of each binary index).

%I A368112 #5 Dec 18 2023 08:28:46
%S A368112 1,4,20,52,64,68,84,116,308,372,820,884,1088,1092,1108,1140,1396,1908,
%T A368112 2868,2932,3956,5184,5188,5204,5236,5492,6004,8052,13376,13380,13396,
%U A368112 13428,13684,14196,16244,17204,17268,18292,19252,19316,20340,22388,24436,30580
%N A368112 Sorted positions of first appearances in A368109 (number of ways to choose a binary index of each binary index).
%C A368112 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 A368112 The terms together with the corresponding set-systems begin:
%e A368112     1: {{1}}
%e A368112     4: {{1,2}}
%e A368112    20: {{1,2},{1,3}}
%e A368112    52: {{1,2},{1,3},{2,3}}
%e A368112    64: {{1,2,3}}
%e A368112    68: {{1,2},{1,2,3}}
%e A368112    84: {{1,2},{1,3},{1,2,3}}
%e A368112   116: {{1,2},{1,3},{2,3},{1,2,3}}
%e A368112   308: {{1,2},{1,3},{2,3},{1,4}}
%e A368112   372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}
%e A368112   820: {{1,2},{1,3},{2,3},{1,4},{2,4}}
%e A368112   884: {{1,2},{1,3},{2,3},{1,2,3},{1,4},{2,4}}
%t A368112 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A368112 c=Table[Length[Tuples[bpe/@bpe[n]]], {n,1000}];
%t A368112 Select[Range[Length[c]], FreeQ[Take[c,#-1],c[[#]]]&]
%Y A368112 For multisets we have A367915, unsorted A367913, firsts A367912.
%Y A368112 Sorted positions of first appearances in A368109.
%Y A368112 The unsorted version is A368111.
%Y A368112 A048793 lists binary indices, length A000120, sum A029931.
%Y A368112 A058891 counts set-systems, covering A003465, connected A323818.
%Y A368112 A070939 gives length of binary expansion.
%Y A368112 A096111 gives product of binary indices.
%Y A368112 Cf. A072639, A253317, A326031, A326702, A326753, A355741, A367771, A367905, A367906, A367911, A368184.
%K A368112 nonn
%O A368112 1,2
%A A368112 _Gus Wiseman_, Dec 17 2023