A266346 - OEIS

%I #21 Oct 08 2016 17:01:20

%S 0,1,4,6,9,16,20,24,25,28,30,35,36,42,49,64,72,80,81,88,90,96,99,100,

%T 104,108,110,112,117,120,121,126,130,132,135,140,143,144,150,154,156,

%U 165,168,169,180,182,195,196,210,225,256,272,288,289,304,306,320,323,324,336,340,342,352,357,360,361,368,374,378,380,384,391

%N Numbers that can be represented as a product of two numbers with an equal number of significant digits (bits) in binary system.

%C Indexing starts from zero as a(0) = 0 is a special case in this sequence.

%H Antti Karttunen, <a href="/A266346/b266346.txt">Table of n, a(n) for n = 0..9616</a>

%e 1 can be represented as 1*1 (1 being "1" also in base-2 system), thus it is included.

%e 4 can be represented as 2*2, and like any square, is included.

%e 6 can be represented as 2*3, and both "10" and "11" require two bits in binary system, thus 6 is included.

%t {0}~Join~Flatten[Position[#, k_ /; k > 0] &@ Table[Length@ DeleteCases[Flatten@ Map[Differences@ IntegerLength[#, 2] &, Transpose@ {#, n/#}] &@ TakeWhile[Divisors@ n, # <= Sqrt@ n &], k_ /; k > 0], {n, 400}]] (* _Michael De Vlieger_, Dec 30 2015 *)

%Y Positions of nonzeros in A266342.

%Y Cf. A266347 (complement).

%Y Cf. A000290, A085721, A261073, A261074, A261075 (subsequences).

%Y Cf. also A266342.

%K nonn,base,look

%O 0,3

%A _Antti Karttunen_, Dec 28 2015