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A327281 Numbers less than the maximum possible determinant A301371(8)=27296640 not occurring as determinant of an 8 X 8 matrix whose entries are a permutation of the multiset {1^8,..,8^8}.

%I A327281 #49 Sep 24 2019 02:59:32
%S A327281 27003797,27011623,27012187,27012757,27012835
%N A327281 Numbers less than the maximum possible determinant A301371(8)=27296640 not occurring as determinant of an 8 X 8 matrix whose entries are a permutation of the multiset {1^8,..,8^8}.
%C A327281 The sequence terms are based on numerical results. No proof for the non-existence of a matrix with given determinant value less than Gasper's upper bound (see Corollary 3 in Sigg) is known. The number of sequence terms is <= 205426. Candidates for a continuation of the sequence are provided as external file.
%H A327281 <a href="/A327281/b327281.txt">Table of n, a(n) for n = 1..5</a>
%H A327281 Hugo Pfoertner, <a href="/A327281/a327281.pdf">Plot of sequence</a>.
%H A327281 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a327281.txt">Conjectured continuation of A327281</a>, (2019).
%H A327281 Markus Sigg, <a href="https://arxiv.org/abs/1804.02897">Gasper's determinant theorem, revisited</a>, arXiv:1804.02897 [math.CO], 2018.
%e A327281 The following matrices have determinants in the vicinity of a(1) = A322576(8) = 27003797, for which no corresponding matrix is known:
%e A327281 27003795 = det[2,5,1,4,8,7,3,6; 3,2,4,8,5,5,8,2; 7,1,7,3,4,8,2,4; 8,7,1,4,2,5,6,3; 1,6,7,3,1,6,6,6; 4,8,7,5,6,3,2,1; 5,3,5,1,7,1,7,6; 5,4,4,8,3,2,2,8],
%e A327281 27003796 = det[1,5,6,3,7,4,8,2; 6,4,8,2,2,8,3,3; 4,1,2,3,6,7,5,8; 5,5,2,8,6,7,3,1; 8,6,2,3,2,3,8,4; 1,6,5,7,1,4,4,7; 5,8,4,2,7,3,1,6; 6,1,7,7,5,1,4,5],
%e A327281 27003798 = det[7,4,2,8,7,3,1,5; 3,6,6,1,8,2,4,6; 2,1,3,5,6,8,6,5; 6,5,7,3,3,8,1,3; 5,2,8,6,4,2,7,2; 8,3,3,2,2,4,6,8; 1,7,5,7,1,4,4,7; 5,8,1,4,4,5,7,1],
%e A327281 27003799 = det[2,8,6,4,7,1,5,4; 5,7,1,8,1,4,6,4; 5,3,7,3,3,6,8,1; 2,3,8,6,2,5,2,7; 3,4,2,1,5,7,6,8; 8,7,5,2,4,6,1,4; 3,3,3,7,8,7,2,2; 8,1,4,5,6,1,5,6].
%Y A327281 Cf. A301371, A322576, A325900.
%K A327281 nonn,fini,more,hard
%O A327281 1,1
%A A327281 _Hugo Pfoertner_, Sep 20 2019