id:A083567 - OEIS Search Results

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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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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; listen)

	OFFSET	`1,1`
	COMMENT	`This is the sequence of n such that the average of ones in binary expansion of n is the same of the average of ones in binary expansion of n^2. Conjecture.` `The counting function p(n) p(n)=c n/log n + o(n/log n).`
	REFERENCES	`G. Melfi, On a family of positive integer sequences, in preparation.`
	EXAMPLE	`a(1)=21 because 21=(10101) and 441=(110111001) and no smaller integer has the property that 2B(n)=B(n^2).`
	CROSSREFS	`Cf. A077436.` `Sequence in context: A043751 A043759 A043768 this_sequence A109211 A050782 A061906` `Adjacent sequences: A083564 A083565 A083566 this_sequence A083568 A083569 A083570`
	KEYWORD	`easy,nonn`
	AUTHOR	`Giuseppe Melfi (Giuseppe.Melfi(AT)unine.ch), Jun 13 2003`

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Last modified November 30 13:13 EST 2009. Contains 167758 sequences.

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