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A362289
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a(n) is the largest denominator when the greedy algorithm for Egyptian fractions is applied to 1/n + 1/(n+1).
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0
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2, 3, 12, 180, 30, 1428, 56, 2520, 90, 2310, 132, 100292556, 182, 9240, 240, 119952, 306, 614444040, 380, 23100, 462, 42190274940, 552, 77390453400, 650, 201474, 756, 23370247110, 870, 200880, 992, 14523137084239067683872, 1122, 2206260, 1260, 104845560637757648698080
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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For n=16, 1/16 + 1/17 = 33/272 which written in Egyptian fractions is 1/9 + 1/98 + 1/119952 and the largest denominator is 119952.
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MATHEMATICA
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egyptFraction[f_] := Ceiling[1/Most[NestWhileList[# - 1/Ceiling[1/#] &, f, # != 0 &]]]; a[n_] := egyptFraction[1/n + 1/(n + 1)][[-1]]; Array[a, 40] (* Amiram Eldar, Apr 14 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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