A371732 - OEIS

A371732

Numbers n such that each binary index k (from row n of A048793) has the same sum of binary indices A029931(k).

1, 2, 4, 8, 12, 16, 32, 64, 128, 144, 256, 288, 512, 576, 1024, 2048, 3072, 4096, 8192, 16384, 32768, 32800, 33024, 33056, 65536, 65600, 66048, 66112, 131072, 132096, 133120, 134144, 262144, 266240, 524288, 528384, 786432, 790528, 1048576, 1056768, 2097152

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..41.

EXAMPLE

The terms together with their binary expansions and binary indices begin:

1: 1 ~ {1}

2: 10 ~ {2}

4: 100 ~ {3}

8: 1000 ~ {4}

12: 1100 ~ {3,4}

16: 10000 ~ {5}

32: 100000 ~ {6}

64: 1000000 ~ {7}

128: 10000000 ~ {8}

144: 10010000 ~ {5,8}

256: 100000000 ~ {9}

288: 100100000 ~ {6,9}

512: 1000000000 ~ {10}

576: 1001000000 ~ {7,10}

1024: 10000000000 ~ {11}

2048: 100000000000 ~ {12}

3072: 110000000000 ~ {11,12}

4096: 1000000000000 ~ {13}

8192: 10000000000000 ~ {14}

16384: 100000000000000 ~ {15}

32768: 1000000000000000 ~ {16}

32800: 1000000000100000 ~ {6,16}

MATHEMATICA

bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

Select[Range[1000], SameQ@@Total/@bix/@bix[#]&]

CROSSREFS

For prime instead of binary indices we have A326534.

A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.

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

A070939 gives length of binary expansion.

A096111 gives product of binary indices.

A321142 and A371794 count non-biquanimous strict partitions.

A321452 counts quanimous partitions, ranks A321454.

A326031 gives weight of the set-system with BII-number n.

A357976 ranks the biquanimous partitions counted by A002219 aerated.

A371731 ranks the non-biquanimous partitions counted by A371795, A006827.

Cf. A035470, A038041, A237258, A320324, A321453, A321455, A326518, A336137, A371783, A371791, A371796.

Sequence in context: A266047 A375599 A324214 * A368507 A273109 A046843

Adjacent sequences: A371729 A371730 A371731 * A371733 A371734 A371735

KEYWORD

nonn,base

AUTHOR

Gus Wiseman, Apr 13 2024

STATUS

approved