# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a367912
Showing 1-1 of 1

%I A367912 #12 Dec 28 2023 09:22:07
%S A367912 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 A367912 2,2,4,4,4,4,2,2,2,2,4,4,4,4,4,4,4,4,7,7,7,7,4,4,4,4,7,7,7,7,3,3,3,3,
%U A367912 5,5,5,5,3,3,3,3,5,5,5,5,5,5,5,5,8,8,8,8
%N A367912 Number of multisets that can be obtained by choosing a binary index of each binary index of n.
%C A367912 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 A367912 The run-lengths are all 4 or 8.
%e A367912 The binary indices of binary indices of 52 are {{1,2},{1,3},{2,3}}, with multiset choices {1,1,2}, {1,1,3}, {1,2,2}, {1,2,3}, {1,3,3}, {2,2,3}, {2,3,3}, so a(52) = 7.
%t A367912 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]],1];
%t A367912 Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]], {n,0,100}]
%Y A367912 Positions of ones are A253317.
%Y A367912 The version for multisets and divisors is A355733, for sequences A355731.
%Y A367912 The version for multisets is A355744, for sequences A355741.
%Y A367912 For a sequence of distinct choices we have A367905, firsts A367910.
%Y A367912 Positions of first appearances are A367913, sorted A367915.
%Y A367912 Choosing a sequence instead of multiset gives A368109, firsts A368111.
%Y A367912 Choosing a set instead of multiset gives A368183, firsts A368184.
%Y A367912 A048793 lists binary indices, length A000120, sum A029931.
%Y A367912 A058891 counts set-systems, covering A003465, connected A323818.
%Y A367912 A070939 gives length of binary expansion.
%Y A367912 A096111 gives product of binary indices.
%Y A367912 Cf. A072639, A309326, A326031, A326702, A326753, A355735, A355739, A355740, A355745, A367771, A367906.
%K A367912 nonn
%O A367912 0,5
%A A367912 _Gus Wiseman_, Dec 12 2023

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE