A266346 Numbers that can be represented as a product of two numbers with an equal number of significant digits (bits) in binary system.

0, 1, 4, 6, 9, 16, 20, 24, 25, 28, 30, 35, 36, 42, 49, 64, 72, 80, 81, 88, 90, 96, 99, 100, 104, 108, 110, 112, 117, 120, 121, 126, 130, 132, 135, 140, 143, 144, 150, 154, 156, 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

Offset: 0

Author

Antti Karttunen, Dec 28 2015

Keywords

• nonn
• base
• look

Comments

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

Examples

			1 can be represented as 1*1 (1 being "1" also in base-2 system), thus it is included.
4 can be represented as 2*2, and like any square, is included.
6 can be represented as 2*3, and both "10" and "11" require two bits in binary system, thus 6 is included.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..9616

Crossrefs

Positions of nonzeros in A266342.

Cf. A266347 (complement).

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

Cf. also A266342.

Programs

Mathematica

{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 *)