A327269 Smallest modulus of any integer n X n determinant with top row 1,2,...,n and rows nonzero and pairwise orthogonal.

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

Offset: 1

Author

Christopher J. Smyth, Sep 02 2019

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Links

• Chris Pinner and Chris Smyth, Lattices of minimal index in Z^n having an orthogonal basis containing a given basis vector
• Christopher J. Smyth, List of n, a(n) and associated matrix, for n <= 8

Crossrefs

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.