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

0,3

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Positions of nonzeros in A266342.

Cf. A266347 (complement).

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

Cf. also A266342.

Sequence in context: A045114 A010436 A085955 * A181018 A155569 A189484

Adjacent sequences: A266343 A266344 A266345 * A266347 A266348 A266349

Keyword

nonn,base,look

Author

Antti Karttunen, Dec 28 2015

Status

approved