A059774 -id:A059774 - cp's OEIS frontend

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

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

nonn

A form of generalized GCD of 4 numbers.

			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.

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]

Cf. A059804, A059774.

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.

Original entry on oeis.org

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

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

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

Officially these are just conjectures so far.

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]

Cf. A059774, A024450, A047896, A060453.

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

cp's OEIS Frontend

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.

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