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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 (list; graph; refs; listen; history; text; internal format)
 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) LINKS Table of n, a(n) for n=1..6. 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: A358289 A156482 A335832 * A319166 A335400 A304193 Adjacent sequences: A173343 A173344 A173345 * A173347 A173348 A173349 KEYWORD nonn,base,full,fini AUTHOR Vladimir Joseph Stephan Orlovsky, Feb 16 2010 EXTENSIONS Minor edits by N. J. A. Sloane, Feb 21 2010 a(1) = 0 inserted by Michel Marcus, Nov 19 2015 STATUS approved

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Last modified October 3 22:39 EDT 2023. Contains 365872 sequences. (Running on oeis4.)