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A087910
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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.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
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REFERENCES
| A. M. Robert, A Course in p-adic Analysis, Springer, 2000; see p. 278.
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LINKS
| Sydney University Mathematical Society Problems Competition 2002.
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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.
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CROSSREFS
| Cf. A108866.
Sequence in context: A193906 A201972 A202396 * A035570 A183928 A126291
Adjacent sequences: A087907 A087908 A087909 * A087911 A087912 A087913
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KEYWORD
| easy,nonn
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AUTHOR
| Robin Chapman (rjc(AT)maths.ex.ac.uk), Oct 17 2003
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