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A173346
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.
0
0, 4, 16, 144, 324, 625
OFFSET
1,2
COMMENTS
From Rémy Sigrist, Apr 30 2017: (Start)
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)
FORMULA
Terms satisfy m = A071295(m)^2. - Michel Marcus, Nov 19 2015
EXAMPLE
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.
MATHEMATICA
Select[Range[8! ], DigitCount[ #, 2, 0]*DigitCount[ #, 2, 1]==Sqrt[ # ]&]
PROG
(PARI) isok(n) = {n1 = hammingweight(n); n0 = #binary(n) - n1; (n0*n1)^2 == n; } \\ Michel Marcus, Nov 19 2015
CROSSREFS
Cf. A071295.
Sequence in context: A375919 A156482 A335832 * A319166 A335400 A304193
KEYWORD
nonn,base,full,fini
AUTHOR
EXTENSIONS
Minor edits by N. J. A. Sloane, Feb 21 2010
a(1) = 0 inserted by Michel Marcus, Nov 19 2015
STATUS
approved