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A371732
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Numbers n such that each binary index k (from row n of A048793) has the same sum of binary indices A029931(k).
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0
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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
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listen;
history;
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internal format)
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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}
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MATHEMATICA
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bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[1000], SameQ@@Total/@bix/@bix[#]&]
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CROSSREFS
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For prime instead of binary indices we have A326534.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A326031 gives weight of the set-system with BII-number n.
Cf. A035470, A038041, A237258, A320324, A321453, A321455, A326518, A336137, A371783, A371791, A371796.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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