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A266346
Numbers that can be represented as a product of two numbers with an equal number of significant digits (bits) in binary system.
4
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
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
KEYWORD
nonn,base,look
AUTHOR
Antti Karttunen, Dec 28 2015
STATUS
approved