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A173346
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Numbers such that the product of numbers of 0's and 1's in the binary representation is equal to the square root of the number.
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0
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OFFSET
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1,2
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COMMENTS
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In binary:
- the product of numbers of 0's and 1's for an N-digit number is at most N^2/4,
- the least N-digit number is 2^(N-1),
- for N >= 11, (N^2/4)^2 < 2^(N-1).
Hence there are no terms >= 2^10.
(End)
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LINKS
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FORMULA
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EXAMPLE
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625 -> 1001110001; five '0' and five '1'; 5*5=25; sqrt(625)=25.
324 -> 101000100; 3 '0' and 6 '1'; 3*6=18; sqrt(324)=18.
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MATHEMATICA
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Select[Range[8! ], DigitCount[ #, 2, 0]*DigitCount[ #, 2, 1]==Sqrt[ # ]&]
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PROG
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(PARI) isok(n) = {n1 = hammingweight(n); n0 = #binary(n) - n1; (n0*n1)^2 == n; } \\ Michel Marcus, Nov 19 2015
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CROSSREFS
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KEYWORD
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nonn,base,full,fini
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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