A047896 For given n, consider all 4-tuples P = (a,b,c,d) with P.P = n; let d = squared distance to the line OP from the closest point of Z^n (excluding the endpoints); sequence gives max_P d*n.

1, 1, 2, 3, 1, 2, 3, 0, 2, 4, 2, 3, 3, 3, 5, 0, 2, 5, 3, 4, 5, 6, 5, 0, 6, 4, 5, 3, 5, 9, 6, 0, 6, 8, 6, 8, 9, 8, 9, 0, 5, 6, 5, 8, 9, 11, 10, 0, 6, 11, 9, 4, 10, 11, 10, 0, 14, 9, 11, 11, 9, 11, 14, 0, 14, 11, 11, 8, 11, 19, 14, 0, 9, 11, 11, 8, 10, 14, 14, 0, 14, 10, 13, 20, 21

Offset

1,3

Comments

A form of generalized GCD of 4 numbers.

Links

Table of n, a(n) for n=1..85.

N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, Fat Struts: Constructions and a Bound, Proceedings Information Theory Workshop, Taormino, Italy, 2009. [Cached copy]

N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, A Note on Projecting the Cubic Lattice, Discrete and Computational Geometry, Vol. 46 (No. 3, 2011), 472-478.

N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, The Lifting Construction: A General Solution to the Fat Strut Problem, Proceedings International Symposium on Information Theory (ISIT), 2010, IEEE Press. [Cached copy]

Example

n=10, best P is (1,1,2,2), closest point of Z^4 to OP is (0,0,1,1) at squared distance d = 2/5, so a(10) = 10*2/5 = 4.

Crossrefs

Cf. A059804, A059774.

Sequence in context: A205003 A159956 A053839 * A073645 A294180 A179542

Adjacent sequences: A047893 A047894 A047895 * A047897 A047898 A047899

Keyword

nonn

Author

N. J. A. Sloane and Vinay Vaishampayan, Feb 27 2001

Status

approved