cp's OEIS Frontend

A368109 Number of ways to choose a binary index of each binary index of n.

%I A368109 #10 Dec 28 2023 11:31:57
%S A368109 1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4,2,2,2,2,4,4,4,4,2,2,
%T A368109 2,2,4,4,4,4,2,2,2,2,4,4,4,4,4,4,4,4,8,8,8,8,4,4,4,4,8,8,8,8,3,3,3,3,
%U A368109 6,6,6,6,3,3,3,3,6,6,6,6,6,6,6,6,12,12,12
%N A368109 Number of ways to choose a binary index of each binary index of n.
%C A368109 First differs from A367912 at a(52) = 8, A367912(52) = 7.
%C A368109 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}.
%C A368109 Run-lengths are all 4 or 8.
%F A368109 a(n) = Product_{k in A048793(n)} A000120(k).
%e A368109 The binary indices of binary indices of 20 are {{1,2},{1,3}}, with choices (1,1), (1,3), (2,1), (2,3), so a(20) = 4.
%e A368109 The binary indices of binary indices of 52 are {{1,2},{1,3},{2,3}}, with choices (1,1,1), (1,1,3), (1,3,2), (1,3,3), (2,1,2), (2,1,3), (2,3,2), (2,3,3), so a(52) = 8.
%t A368109 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]],1];
%t A368109 Table[Length[Tuples[bpe/@bpe[n]]], {n,0,100}]
%Y A368109 All entries appear to belong to A003586.
%Y A368109 Positions of ones are A253317.
%Y A368109 The version for prime indices is A355741, for multisets A355744.
%Y A368109 Choosing a multiset (not sequence) gives A367912, firsts A367913.
%Y A368109 Positions of first appearances are A368111, sorted A368112.
%Y A368109 A048793 lists binary indices, length A000120, sum A029931.
%Y A368109 A058891 counts set-systems, covering A003465, connected A323818.
%Y A368109 A070939 gives length of binary expansion.
%Y A368109 A096111 gives product of binary indices.
%Y A368109 Cf. A072639, A309326, A326031, A326702, A326753, A355731, A355739, A367771, A367905, A367906, A367915.
%K A368109 nonn
%O A368109 0,5
%A A368109 _Gus Wiseman_, Dec 12 2023