cp's OEIS Frontend

A371732 Numbers n such that each binary index k (from row n of A048793) has the same sum of binary indices A029931(k).

%I A371732 #7 Apr 14 2024 03:49:39
%S A371732 1,2,4,8,12,16,32,64,128,144,256,288,512,576,1024,2048,3072,4096,8192,
%T A371732 16384,32768,32800,33024,33056,65536,65600,66048,66112,131072,132096,
%U A371732 133120,134144,262144,266240,524288,528384,786432,790528,1048576,1056768,2097152
%N A371732 Numbers n such that each binary index k (from row n of A048793) has the same sum of binary indices A029931(k).
%e A371732 The terms together with their binary expansions and binary indices begin:
%e A371732         1:                1 ~ {1}
%e A371732         2:               10 ~ {2}
%e A371732         4:              100 ~ {3}
%e A371732         8:             1000 ~ {4}
%e A371732        12:             1100 ~ {3,4}
%e A371732        16:            10000 ~ {5}
%e A371732        32:           100000 ~ {6}
%e A371732        64:          1000000 ~ {7}
%e A371732       128:         10000000 ~ {8}
%e A371732       144:         10010000 ~ {5,8}
%e A371732       256:        100000000 ~ {9}
%e A371732       288:        100100000 ~ {6,9}
%e A371732       512:       1000000000 ~ {10}
%e A371732       576:       1001000000 ~ {7,10}
%e A371732      1024:      10000000000 ~ {11}
%e A371732      2048:     100000000000 ~ {12}
%e A371732      3072:     110000000000 ~ {11,12}
%e A371732      4096:    1000000000000 ~ {13}
%e A371732      8192:   10000000000000 ~ {14}
%e A371732     16384:  100000000000000 ~ {15}
%e A371732     32768: 1000000000000000 ~ {16}
%e A371732     32800: 1000000000100000 ~ {6,16}
%t A371732 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A371732 Select[Range[1000],SameQ@@Total/@bix/@bix[#]&]
%Y A371732 For prime instead of binary indices we have A326534.
%Y A371732 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A371732 A058891 counts set-systems, A003465 covering, A323818 connected.
%Y A371732 A070939 gives length of binary expansion.
%Y A371732 A096111 gives product of binary indices.
%Y A371732 A321142 and A371794 count non-biquanimous strict partitions.
%Y A371732 A321452 counts quanimous partitions, ranks A321454.
%Y A371732 A326031 gives weight of the set-system with BII-number n.
%Y A371732 A357976 ranks the biquanimous partitions counted by A002219 aerated.
%Y A371732 A371731 ranks the non-biquanimous partitions counted by A371795, A006827.
%Y A371732 Cf. A035470, A038041, A237258, A320324, A321453, A321455, A326518, A336137, A371783, A371791, A371796.
%K A371732 nonn,base
%O A371732 1,2
%A A371732 _Gus Wiseman_, Apr 13 2024