OEIS down? Floor (n^(4/3))

Jonathan Post jvospost3 at gmail.com
Sun Apr 29 21:16:59 CEST 2007


For nearly half an hour my system's been timing out on a search of OEIS for
0, 1, 2, 4, 6, 8, 10, 13, 16, 18, 21, 24, 27, 30, 33, 36, 40, 43, 47,
50, 54, ...
a(n) = Floor(n^(4/3))
which I wanted to comment with a reference to Szekely's 1997 proof
based on Ajtai, Chvatal, Newborn, and Szemeredi's result of Erdos'
question on the number of unit distances among n points in the plane.
Erdos had proven that this is at most n^1+o(1)), that was improved to
c*n^(4/3) by Spencer, Szemeredi, and Trotter, and then Szekely's 1997
proof of that bound "was probably the last proof Erdos judged to have
come from The Book" [Bollabos, AMM, March 1998, p.224].





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