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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.

%I A059804 #12 Jul 02 2025 23:17:31
%S A059804 1,3,9,39,87,215,391,711,1326,1975,2925,4256,5696,7537,9774,12488,
%T A059804 16322,20477,24966,30007,35336,41577,48466,56387,65796,75997,86606,
%U A059804 98055,109936,122705,138834,155995,174764,194085,216286,239087,263736,290305
%N 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.
%C A059804 v.v is given by A024450(n). For n >= 19, a(n) = A024450(n-1).
%C A059804 Officially these are just conjectures so far.
%H A059804 N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/Exists.pdf">Fat Struts: Constructions and a Bound</a>, Proceedings Information Theory Workshop, Taormino, Italy, 2009. [<a href="/A047896/a047896.pdf">Cached copy</a>]
%H A059804 N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/FATS.pdf">A Note on Projecting the Cubic Lattice</a>, Discrete and Computational Geometry, Vol. 46 (No. 3, 2011), 472-478.
%H A059804 N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/main_fat_strut.pdf">The Lifting Construction: A General Solution to the Fat Strut Problem</a>, Proceedings International Symposium on Information Theory (ISIT), 2010, IEEE Press. [<a href="/A047896/a047896_1.pdf">Cached copy</a>]
%Y A059804 Cf. A059774, A024450, A047896, A060453.
%Y A059804 Cf. A137609 (where the minimum distance occurs along the line segment).
%K A059804 nonn,easy,nice
%O A059804 2,2
%A A059804 _N. J. A. Sloane_ and _Vinay Vaishampayan_, Feb 21 2001