A327271 Smallest modulus of any n X n integer determinant whose top row has all 1's and whose rows are pairwise orthogonal.

1, 2, 6, 8, 40, 48, 336, 128, 864, 1280, 8448, 3072, 39936

Offset

1,2

Comments

a(n) = A327267(2^n), since 2^n = (p_1)^n is the Heinz code for the multiset {1,1,...,1}.

See Pinner and Smyth link below for more details, including an algorithm for computing A327267(n). Also, see file link below for {(n, a(n), matrix(n)), n <= 13}, where matrix(n) has minimal modulus determinant equal to a(n) among n X n matrices with top row all 1's and all rows orthogonal.

For the first 13 terms, the number of prime factors counted with multiplicity equals n-1: A001222(a(n))=n-1. How far does this hold? - Jon Maiga, Sep 07 2019

Links

Table of n, a(n) for n=1..13.

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 up to 13

Example

a(3) = 6 because the matrix [[1,1,1],[1,-1,0],[1,1,-2]] has top row of 3 1's and all rows orthogonal, and minimal positive determinant equal to 6.

Crossrefs

Subsequence of A327267, see comments; A327273 is similar, but determinant's top row is 1,2,2^2,...,2^{n-1}.

Sequence in context: A235320 A152158 A291782 * A335111 A337882 A095239

Adjacent sequences: A327268 A327269 A327270 * A327272 A327273 A327274

Keyword

nonn,more

Author

Christopher J. Smyth, Sep 02 2019

Status

approved