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Search: id:A159303
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| A159303 |
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a(n) is the least L^1-norm of a square integer matrix of determinant n. The L^1-norm of the matrix M=(m_i,j) is by definition sum(i,j) |m_i,j|. |
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+0
1
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| 1, 2, 3, 4, 5, 5, 7, 6, 6, 7, 9, 7, 9, 9, 8, 8, 10, 8, 11, 9
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Daniel Goldstein, Alfred Hales and Richard Stong. Light integer matrices of prime determinant. To appear.
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FORMULA
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It is shown in the paper cited above that lim a(p)/lg(p) = 5/2, where the limit is over primes p tending to infinity and where lg is the logarithm base 2.
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EXAMPLE
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a(17) = 10 from the 2-by-2 matrix (4 -1\\1 4). This matrix has determinant 17 and L^1-norm 10 = 4 + 1 + 1 + 4. No square integer matrix has determinant 17 and L^1-norm < 10.
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CROSSREFS
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Sequence in context: A106492 A118503 A086295 this_sequence A001414 A134875 A134889
Adjacent sequences: A159300 A159301 A159302 this_sequence A159304 A159305 A159306
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KEYWORD
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nonn
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AUTHOR
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Daniel Goldstein (dgoldste(AT)ccrwest.org), Apr 09 2009
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