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.

1, 4, 64, 20, 68, 320, 52, 84, 16448, 324, 832, 116, 1104, 308, 816, 340, 836, 848, 1108, 1136, 1360, 3152, 16708, 372, 5188, 5216, 852, 880, 2884, 1364, 13376, 1392, 3184, 3424, 17220, 5204, 5220, 2868, 5728, 884, 19536, 66896, 2900, 1396, 21572, 3188, 3412

Offset

1,2

Comments

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}.

Links

Table of n, a(n) for n=1..47.

Example

The terms together with the corresponding set-systems begin:
      1: {{1}}
      4: {{1,2}}
     64: {{1,2,3}}
     20: {{1,2},{1,3}}
     68: {{1,2},{1,2,3}}
    320: {{1,2,3},{1,4}}
     52: {{1,2},{1,3},{2,3}}
     84: {{1,2},{1,3},{1,2,3}}
  16448: {{1,2,3},{1,2,3,4}}
    324: {{1,2},{1,2,3},{1,4}}
    832: {{1,2,3},{1,4},{2,4}}
    116: {{1,2},{1,3},{2,3},{1,2,3}}

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
spnm[y_]:=Max@@NestWhile[Most, y, Union[#]!=Range[0, Max@@#]&];
c=Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]], {n, 1000}];
Table[Position[c, n][[1, 1]], {n, spnm[c]}]

Crossrefs

A version for multisets and divisors is A355734.

With distinctness we have A367910, firsts of A367905, sorted A367911.

Positions of first appearances in A367912.

The sorted version is A367915.

For sequences we have A368111, firsts of A368109, sorted A368112.

For sets we have A368184, firsts of A368183, sorted A368185.

A048793 lists binary indices, length A000120, sum A029931.

A058891 counts set-systems, covering A003465, connected A323818.

A070939 gives length of binary expansion.

A096111 gives product of binary indices.

Cf. A072639, A309326, A326031, A326702, A326749, A326753, A355733, A355741, A355744.

Sequence in context: A361683 A111444 A368111 * A210935 A090561 A273375

Adjacent sequences: A367910 A367911 A367912 * A367914 A367915 A367916

Keyword

nonn

Author

Gus Wiseman, Dec 16 2023

Status

approved