A367915 Sorted positions of first appearances in A367912 (number of multisets that can be obtained by choosing a binary index of each binary index).

1, 4, 20, 52, 64, 68, 84, 116, 308, 320, 324, 340, 372, 816, 832, 836, 848, 852, 880, 884, 1104, 1108, 1136, 1360, 1364, 1392, 1396, 1904, 1908, 2868, 2884, 2900, 2932, 3152, 3184, 3188, 3412, 3424, 3440, 3444, 3952, 3956, 5188, 5204, 5216, 5220, 5236, 5476

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..48.

Example

The terms together with the corresponding set-systems begin:
     1: {{1}}
     4: {{1,2}}
    20: {{1,2},{1,3}}
    52: {{1,2},{1,3},{2,3}}
    64: {{1,2,3}}
    68: {{1,2},{1,2,3}}
    84: {{1,2},{1,3},{1,2,3}}
   116: {{1,2},{1,3},{2,3},{1,2,3}}
   308: {{1,2},{1,3},{2,3},{1,4}}
   320: {{1,2,3},{1,4}}
   324: {{1,2},{1,2,3},{1,4}}
   340: {{1,2},{1,3},{1,2,3},{1,4}}
   372: {{1,2},{1,3},{2,3},{1,2,3},{1,4}}

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
c=Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]], {n, 10000}];
Select[Range[Length[c]], FreeQ[Take[c, #-1], c[[#]]]&]

Crossrefs

A version for multisets and divisors is A355734.

Sorted positions of first appearances in A367912, for sequences A368109.

The unsorted version is A367913.

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, A355744, A367905, A367906, A367911, A368112, A368185.

Sequence in context: A294630 A160799 A187274 * A368112 A108099 A244050

Adjacent sequences: A367912 A367913 A367914 * A367916 A367917 A367918

Keyword

nonn

Author

Gus Wiseman, Dec 16 2023

Status

approved