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Exponent of the greatest power of 2 dividing the numerator of 2^1/1 + 2^2/2 + 2^3/3 + ... + 2^n/n.

+0
2

1, 2, 2, 5, 8, 5, 5, 13, 9, 10, 10, 12, 12, 12, 12, 22, 17, 18, 18, 21, 22, 21, 21, 27, 25, 26, 26, 27, 27, 27, 27, 40, 33, 34, 34, 37, 39, 37, 37, 48, 41, 42, 42, 44, 44, 44, 44, 54, 49, 50, 50, 53, 54, 53, 53, 58, 57, 59, 62, 58, 58, 58 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`Problem 9 of the 2002 Sydney University Mathematical Society Problems competition asked for a proof that a(n) tends to infinity with n. While this is immediate from the theory of the 2-adic logarithm, elementary proofs are available`
	REFERENCES	`A. M. Robert, A Course in p-adic Analysis, Springer, 2000; see p. 278.`
	LINKS	`Sydney University Mathematical Society Problems Competition 2002.`
	EXAMPLE	`a(5) = 8 as 2^1/1 + 2^2/2 + 2^3/3 + 2^4/4 + 2^5/5 = 256/15 whose numerator is divisible by 2^8 but not by 2^9.`
	CROSSREFS	`Cf. A108866.` `Sequence in context: A074476 A011021 A077232 this_sequence A035570 A126291 A056224` `Adjacent sequences: A087907 A087908 A087909 this_sequence A087911 A087912 A087913`
	KEYWORD	`easy,nonn`
	AUTHOR	`Robin Chapman (rjc(AT)maths.ex.ac.uk), Oct 17 2003`

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.

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