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A092965
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Greatest prime arising as the product of numbers chosen from among the first n numbers + 1.
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5
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2, 3, 7, 13, 61, 241, 2521, 20161, 72577, 604801, 39916801, 59875201, 3113510401, 17435658241, 186810624001, 10461394944001, 118562476032001, 246245142528001, 24329020081766401, 304112751022080001
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OFFSET
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1,1
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COMMENTS
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There are a maximum of 2^n numbers which arise as the products of the subsets of the first n natural numbers. The actual number is smaller because of repetitions. Then a(n) = the greatest prime obtained on adding 1 to each of these numbers.
Different from A089136 (see the comments there).
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LINKS
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EXAMPLE
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a(5) = 61 = 3*4*5 + 1. 5! + 1, 4!+ 1, are composite and 2*4*5 + 1 = 41 <61, etc.
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MATHEMATICA
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Do[l = Map[Times @@ #&, Subsets[Range[n]]]; Print[Max[Select[Map[ #+1&, l], PrimeQ]]], {n, 20}] (* Ryan Propper, Aug 13 2005 *)
f[n_] := Max@ Select[ Union[ Times @@@ Subsets@ Range@ n] + 1, PrimeQ]; Array[f, 20] (* Robert G. Wilson v, Nov 13 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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