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Search: id:A087908
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| A087908 |
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Largest integer not expressible as a nonnegative linear combination of n and n^2+1. |
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+0
1
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| -1, 3, 17, 47, 99, 179, 293, 447, 647, 899, 1209, 1583, 2027, 2547, 3149, 3839, 4623, 5507, 6497, 7599, 8819
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Robert W. Owens, An Algorithm to Solve the Frobenius Problem, Math. Mag. 76(2003),264-275.
A. Brauer and J.E. Shockley, On a Problem of Frobenius, J. reine angew. Math. 211(1962),215-220.
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LINKS
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M. Beck and S. Zack, Refined upper bounds for the Diophantine problem of Frobenius
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FORMULA
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a(n)=n^3-n^2-1 [this follows from the well-known fact that the largest integer not expressible as a nonnegative linear combination of a and b is the number ab-a-b - Matthias Beck (beck(AT)math.sfsu.edu), Sep 22, 2005]
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EXAMPLE
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For n=2, we have to consider nonnegative linear combinations of 2 and 5. Now 3 is not such a combination, but 4=2*2 and 5=1*5, and any positive integer greater than 3 is of the form 2a+b where a and b are nonnegative integers with b equal to 4 or 5. Therefore a(2)=3.
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MAPLE
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with (combinat):seq(n^3-fibonacci(3, n), n=1..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2008
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CROSSREFS
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Adjacent sequences: A087905 A087906 A087907 this_sequence A087909 A087910 A087911
Sequence in context: A106256 A091624 A106078 this_sequence A117012 A095697 A084069
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KEYWORD
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sign
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Oct 15 2003
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