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A051404
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Neither 4 nor 9 divides C(2n-1,n) (almost certainly finite).
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1
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1, 2, 3, 4, 6, 9, 10, 12, 18, 33, 34, 36, 40, 64, 66, 192, 256, 264, 272, 513, 514, 516, 576, 768, 1026, 1056, 2304, 16392, 65664, 81920, 532480, 545259520
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OFFSET
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1,2
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COMMENTS
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Complete up to 2^64 = 18446744073709551616.
Complete up to 2^30000. - Don Reble, Oct 27 2013
A number n is in the sequence if and only if the following inequalities hold s_2(n) <= 2 and s_3(n) + s_3(n-1) - s_3(2*n-1) <= 2, where s_m(n) is sum of digits of n in base m. - Vladimir Shevelev, Oct 30 2013
Equivalently, a number n is in the sequence if and only if there is at most 1 "carry" when adding n and n-1 in both base-2 arithmetic and base-3 arithmetic. - Tom Edgar, Oct 31 2013
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REFERENCES
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A.-M. Legendre, Théorie de Nombres, Firmin Didot Frères, Paris, 1830.
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LINKS
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Table of n, a(n) for n=1..32.
E. E. Kummer, Uber die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew Math. 44 (1852), 93-146.
Don Reble, A051404, SeqFan Post, Oct 30 2013
V. Shevelev, Binomial coefficient predictors, J. of integer sequences, Vol. 14 (2011), Article 11.2.8.
Vladimir Shevelev, Re: A051404, SeqFan Post, Oct 30 2013
Wikipedia, Kummer's Theorem
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EXAMPLE
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For n=64 we have s_2(64)=1, s_3(n)=4, s_3(64-1)=3, s_3(2*64-1)=5 and 4+3-5=2. So 64 is in the sequence. - Vladimir Shevelev, Oct 30 2013
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CROSSREFS
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Sequence in context: A014851 A177919 A128399 * A046097 A239580 A337724
Adjacent sequences: A051401 A051402 A051403 * A051405 A051406 A051407
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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