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A180127
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Upper bound for the determinant of an n X n matrix whose elements are a permutation of the first n^2 prime numbers.
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1
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2, 32, 7414, 4993844, 5761178228, 11320943775475, 35966786849223443, 154715716383037989022, 1041732064414822689366009, 8436103376958505162325231670, 95816938885687281564299004113250
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OFFSET
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1,1
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COMMENTS
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a(n) is an upper bound for A180128(n).
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LINKS
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Table of n, a(n) for n=1..11.
Ortwin Gasper, Hugo Pfoertner and Markus Sigg, An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum JIPAM, Vol. 10, Iss. 3, Art. 63, 2008
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FORMULA
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Let c=A007504(n^2)/n [(1/n)*sum of first n^2 primes]
and d=A024450(n^2)/n [(1/n)*sum of first n^2 squares of primes]
Then a(n)=floor(c*sqrt((d-t)^(n-1))) with t=(c^2-d)/(n-1).
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CROSSREFS
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Cf. A180128 [Maximal determinant of matrix with first n^2 primes], A085000 [Maximal determinant of matrix with elements 1, ..., n^2], A180087 [Upper bound for A085000], A007504 [Sum of first n primes], A024450 [Sum of first n squares of primes]
Sequence in context: A247859 A202629 A129349 * A091804 A012853 A128146
Adjacent sequences: A180124 A180125 A180126 * A180128 A180129 A180130
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner, Aug 12 2010
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STATUS
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approved
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