1,2

An algorithm for generating a(n) is given in the Pinner and Smyth link, where more details about a(n) can be found.

Also, see file link below for {(n,a(n),matrix(n)),0 <= n <= 6}, where matrix(n) has minimal modulus determinant equal to a(n) among (n+1) X (n+1) matrices with top row 1,2,2^2,...,2^n and all rows orthogonal.

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 0 <= n <= 6

a(n) =A327267(Product_{k=0..n} prime(2^k)) =A327267(A325782(n+1)).

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

Subsequence ofA327267-- see comments;A327269is similar, but determinant's top row is 1,2,...,n;A327271is similar, but determinant's top row consists of n 1's.

Sequence in context:A126765A228793A330628*A024492A217805A217808

Adjacent sequences:A327269A327270A327271*A327273A327274A327275

nonn,more

Christopher J. Smyth,Sep 09 2019

approved