A159303 a(n) is the least L^1-norm of a square integer matrix of determinant n. The L^1-norm of the matrix M=(m_i,j) is by definition sum(i,j) |m_i,j|.

1, 2, 3, 4, 5, 5, 7, 6, 6, 7, 9, 7, 9, 9, 8, 8, 10, 8, 11, 9

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Daniel Goldstein, Alfred W. Hales, Richard A. Stong, Light matrices of prime determinant, Proc. Am. Math. Soc. 142 (2014) 805-819

Formula

It is shown in the paper cited above that lim a(p)/lg(p) = 5/2, where the limit is over primes p tending to infinity and where lg is the logarithm base 2.

Example

a(17) = 10 from the 2-by-2 matrix (4 -1\\1 4). This matrix has determinant 17 and L^1-norm 10 = 4 + 1 + 1 + 4. No square integer matrix has determinant 17 and L^1-norm < 10.

Crossrefs

Sequence in context: A086295 A360269 A345423 * A262049 A337310 A001414

Adjacent sequences: A159300 A159301 A159302 * A159304 A159305 A159306

Keyword

nonn

Author

Daniel Goldstein (dgoldste(AT)ccrwest.org), Apr 09 2009

Status

approved