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A083567
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Let B(n) be the number of binary digits in n. This is the sequence of positive integers n such that 2B(n)=B(n^2).
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1
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21, 37, 42, 45, 53, 69, 73, 74, 81, 83, 84, 90, 106, 133, 137, 138, 141, 146, 148, 155, 161, 162, 165, 166, 168, 177, 180, 211, 212, 261, 265, 266, 269, 273, 274, 276, 281, 282, 289, 291, 292, 295, 296, 299, 310, 321, 322, 324, 330, 332, 336, 354, 359, 360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is the sequence of n such that the average of ones in the binary expansion of n is the same of the average of ones in binary expansion of n^2. Conjecture: The counting function p(n) satisfies p(n)=c n/log n + o(n/log n).
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REFERENCES
| G. Melfi, On a family of positive integer sequences, in preparation.
G. Melfi, Su alcune successioni di interi, http://melfi.150m.com/presentazione.pdf.
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EXAMPLE
| a(1)=21 because 21=(10101) and 441=(110111001) and no smaller integer has the property that 2B(n)=B(n^2).
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CROSSREFS
| Cf. A077436.
Sequence in context: A043751 A043759 A043768 * A109211 A050782 A061906
Adjacent sequences: A083564 A083565 A083566 * A083568 A083569 A083570
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KEYWORD
| easy,nonn
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AUTHOR
| Giuseppe Melfi (Giuseppe.Melfi(AT)unine.ch), Jun 13 2003
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