The sparse ruler constant

Find the limit of F(N)/√N, where F(N) is the fewest marks on a ruler of length N that measures every distance; it lies in [1.56, √3].

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "combinatorics",
	5	+ "number-theory"
	6	+ ],
	7	+ "type": "construction",
	8	+ "also": [
	9	+ "proof"
	10	+ ],
	11	+ "source": {
	12	+ "key": "erdos",
	13	+ "name": "Erdős Problems",
	14	+ "url": "https://www.erdosproblems.com/170",
	15	+ "id": "170",
	16	+ "curator": "Thomas Bloom",
	17	+ "poser": "Paul Erdős",
	18	+ "status": "open",
	19	+ "as_of": "2026-10-20",
	20	+ "catalog": "0521c19bbd38"
	21	+ }
	22	+}