A059804 Consider the line segment in R^n from the origin to the point v=(2,3,5,7,11,...) with prime coordinates; let d = squared distance to this line from the closest point of Z^n (excluding the endpoints). Sequence gives d times v.v.

1, 3, 9, 39, 87, 215, 391, 711, 1326, 1975, 2925, 4256, 5696, 7537, 9774, 12488, 16322, 20477, 24966, 30007, 35336, 41577, 48466, 56387, 65796, 75997, 86606, 98055, 109936, 122705, 138834, 155995, 174764, 194085, 216286, 239087, 263736, 290305

Offset

2,2

Comments

v.v is given by A024450(n). For n >= 19, a(n) = A024450(n-1).

Officially these are just conjectures so far.

Links

Table of n, a(n) for n=2..39.

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]

Crossrefs

Cf. A059774, A024450, A047896, A060453.

Cf. A137609 (where the minimum distance occurs along the line segment).

Sequence in context: A225960 A020121 A270593 * A065657 A296102 A149026

Adjacent sequences: A059801 A059802 A059803 * A059805 A059806 A059807

Keyword

nonn,easy,nice

Author

N. J. A. Sloane and Vinay Vaishampayan, Feb 21, 2001

Status

approved