

A327272


Smallest modulus of any (n+1) X (n+1) integer determinant whose top row is 1,2,2^2,...,2^n and whose rows are pairwise orthogonal.


4




OFFSET

1,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..7.
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


FORMULA

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


EXAMPLE

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.


CROSSREFS

Subsequence of A327267 see comments; A327269 is similar, but determinant's top row is 1,2,...,n; A327271 is similar, but determinant's top row consists of n 1's.
Sequence in context: A082145 A126765 A228793 * A024492 A217805 A217808
Adjacent sequences: A327268 A327269 A327271 * A327273 A327274 A327275


KEYWORD

nonn,more


AUTHOR

Christopher J. Smyth, Sep 09 2019


STATUS

approved



