cp's OEIS Frontend

A180128 Maximal determinant of an n X n matrix whose elements are a permutation of the first n^2 prime numbers.

%I A180128 #18 Jan 19 2022 19:27:01
%S A180128 1,2,29,6640,4868296,5725998504,11305600374272,35954639671827328
%N A180128 Maximal determinant of an n X n matrix whose elements are a permutation of the first n^2 prime numbers.
%C A180128 The terms a(5), a(6), a(7) were found by tabu search, with strong numerical evidence for the optimality of a(7).
%C A180128 A known lower bound for the next term a(8) is 154665569137423060000.
%C A180128 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.
%C A180128 An improved lower bound is a(8) >= 154671943501236284416, provided in a private communication by Richard Gosiorovsky. - _Hugo Pfoertner_, Aug 27 2021
%H A180128 Ortwin Gasper, Hugo Pfoertner and Markus Sigg, <a href="http://www.emis.de/journals/JIPAM/article1119.html?sid=1119">An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum</a> JIPAM, Vol. 10, Iss. 3, Art. 63, 2008
%H A180128 Markus Sigg, <a href="https://arxiv.org/abs/1804.02897">Gasper's determinant theorem, revisited</a>, arXiv:1804.02897 [math.CO]
%H A180128 <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>
%e A180128 a(2) = 29:
%e A180128 . 7 3
%e A180128 . 2 5
%e A180128 a(3) = 6640:
%e A180128 . 23 11  5
%e A180128 .  3 17 13
%e A180128 .  7  2 19
%e A180128 a(4) = 4868296:
%e A180128 . 53 11 23 13
%e A180128 . 17 47 29  3
%e A180128 .  7  5 43 37
%e A180128 . 19 31  2 41
%e A180128 a(5) = 5725998504
%e A180128 . 89 41 23  2 53
%e A180128 . 31 97 29 47 11
%e A180128 . 59 13 79 61  7
%e A180128 . 37 19  5 83 67
%e A180128 .  3 43 71 17 73
%e A180128 a(6) = 11305600374272:
%e A180128 . 137  73   7  89  83  13
%e A180128 .  79 139  67  19   3  97
%e A180128 . 101   5 149  61  37  53
%e A180128 .   2 109 103  71 113  11
%e A180128 .  59  29  41  17 131 127
%e A180128 .  23  47  43 151  31 107
%e A180128 a(7) = 35954639671827332:
%e A180128 . 227  71 173  43  83  29  73
%e A180128 . 151 163   5 181   2 103  89
%e A180128 .  31 223 139  61 137  97  13
%e A180128 .  23  47 157 211 109  19 131
%e A180128 . 113   7  67 127 167 199  17
%e A180128 .  53  79 149  37  11 193 179
%e A180128 . 101 107   3  41 191  59 197
%Y A180128 Cf. A180127 [upper bounds for a(n)], A085000 [maximal determinants for matrix elements 1, ..., n^2].
%Y A180128 Cf. A340923, A340924, A340925.
%K A180128 nonn,hard,more
%O A180128 0,2
%A A180128 _Hugo Pfoertner_, Aug 11 2010
%E A180128 a(7) corrected, based on private communication from Richard Gosiorovsky by _Hugo Pfoertner_, Aug 27 2021
%E A180128 a(0)=1 prepended by _Alois P. Heinz_, Jan 19 2022