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A180127 Upper bound for the determinant of an n X n matrix whose elements are a permutation of the first n^2 prime numbers. 1
2, 32, 7414, 4993844, 5761178228, 11320943775475, 35966786849223443, 154715716383037989022, 1041732064414822689366009, 8436103376958505162325231670, 95816938885687281564299004113250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is an upper bound for A180128(n).

LINKS

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

FORMULA

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).

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Aug 12 2010

STATUS

approved

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Last modified January 18 11:48 EST 2021. Contains 340254 sequences. (Running on oeis4.)