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A180128 Maximal determinant of an n X n matrix whose elements are a permutation of the first n^2 prime numbers. 2
2, 29, 6640, 4868296, 5725998504, 11305600374272, 35954639671827332 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The terms a(5), a(6), a(7) were found by tabu search, with strong numerical evidence for the optimality of a(7).

A known lower bound for the next term a(8) is 154665569137423060000.

Upper bounds for higher terms can be found by the method described by O. Gasper, H. Pfoertner and M. Sigg, and are given in A180127, e.g. a(8)<=154715716383037989022.

LINKS

Table of n, a(n) for n=1..7.

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

Markus Sigg, Gasper's determinant theorem, revisited, arXiv:1804.02897 [math.CO]

Index entries for sequences related to maximal determinants

EXAMPLE

a(2)=29:

. 7 3

. 2 5

a(3)=6640:

. 23 11 5

. 3 17 13

. 7 2 19

a(4)=4868296:

. 53 11 23 13

. 17 47 29 3

. 7 5 43 37

. 19 31 2 41

a(5)=5725998504

. 89 41 23 2 53

. 31 97 29 47 11

. 59 13 79 61 7

. 37 19 5 83 67

. 3 43 71 17 73

a(6)=11305600374272:

. 137 73 7 89 83 13

. 79 139 67 19 3 97

. 101 5 149 61 37 53

. 2 109 103 71 113 11

. 59 29 41 17 131 127

. 23 47 43 151 31 107

a(7)=35954639671827332:

. 227 71 173 43 83 29 73

. 151 163 5 181 2 103 89

. 31 223 139 61 137 97 13

. 23 47 157 211 109 19 131

. 113 7 67 127 167 199 17

. 53 79 149 37 11 193 179

. 101 107 3 41 191 59 197

CROSSREFS

Cf. A180127 [upper bounds for a(n)], A085000 [maximal determinants for matrix elements 1, ..., n^2]

Sequence in context: A252042 A295426 A114533 * A087194 A331427 A058988

Adjacent sequences:  A180125 A180126 A180127 * A180129 A180130 A180131

KEYWORD

hard,nonn

AUTHOR

Hugo Pfoertner, Aug 11 2010

STATUS

approved

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Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)