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Revision History for A124255
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Forest-and-trees problem: square of distance to most distant visible tree.
(history; published version)
(history; published version)
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COMMENTS
It is known that, for any coprime x and y, the closest point to the line from (0,0) to (x,y) is 1/sqrt(x^2 + y^2) units away from it (see e.g. the first linked paper in A047896). Since tree trunks intersect lines that are closer than 1/n units, we must have that a(n) < n^2. In addition, a(n) cannot be divisible by the square of any prime p not congruent to 1 modulo 4, since this forces x and y to have common factor p. Combining this with the criteria for a(n) to be a sum of two squares, we have that a(n) is the largest number < n^2 that is either a product of primes congruent to 1 modulo 4 or twice such a product. - Charlie Neder, Jan 15 2019
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LINKS
A different but related problem is addressed at <a href="httphttps://web.archive.org/web/20090706200009/acm
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AUTHOR
_Jon E. Schoenfield (jonscho(AT)hiwaay.net), _, Oct 22 2006
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