A327269 - OEIS

%I #16 Nov 28 2019 07:53:42

%S 1,5,42,90,990,5733,6720,39168

%N Smallest modulus of any integer n X n determinant with top row 1,2,...,n and rows nonzero and pairwise orthogonal

%C Also a(n) = A327267(p_1...p_n), with p_j = j-th prime, since p_1...p_n is the Heinz code for the multiset {1,2,3,...,n}. For more details see Pinner and Smyth link.

%H Chris Pinner and Chris Smyth, <a href="https://www.maths.ed.ac.uk/~chris/papers/MinimalLattices040919.pdf">Lattices of minimal index in Z^n having an orthogonal basis containing a given basis vector</a>

%H Christopher J. Smyth, <a href="/A327269/a327269.pdf">List of n, a(n) and associated matrix, for n <= 8</a>

%e a(3)=42 since det([1,2,3],[1,-2,1],[4,1,-2]) = 42 and is the smallest positive determinant with top row [1,2,3] and all rows orthogonal.

%Y Subsequence of A327267-- see comments; A327271 is similar, but determinant's top row is n 1's; A327272 is similar, but determinant's top row is 1,2,2^2,...,2^n.

%K nonn,more

%O 1,2

%A _Christopher J. Smyth_, Sep 02 2019