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A208643
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Least positive integer m such that those k*(k-1) mod m with k=1,...,n are pairwise distinct.
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13
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1, 3, 5, 7, 11, 11, 13, 16, 17, 19, 23, 23, 29, 29, 29, 31, 37, 37, 37, 41, 41, 43, 47, 47, 53, 53, 53, 59, 59, 59, 61, 64, 67, 67, 71, 71, 73, 79, 79, 79, 83, 83, 89, 89, 89, 97, 97, 97, 97, 101, 101, 103, 107, 107, 109, 113, 113, 127, 127, 127
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OFFSET
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1,2
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COMMENTS
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On Feb. 29, 2012, Zhi-Wei Sun proved that a(n) = min{m>2n-2: m is a prime or a power of two}. He also showed that if we replace k(k-1) in the definition of a(n) by 2k(k-1) then a(n) is the least prime greater than 2n-2 for every n=2,3,4,....
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LINKS
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Zhi-Wei Sun, Table of n, a(n) for n = 1..500
Zhi-Wei Sun, A function taking only prime values, a message to Number Theory List, Feb. 21, 2012.
Zhi-Wei Sun, On functions taking only prime values, J. Number Theory 133(2013), no.8, 2794-2812.
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MATHEMATICA
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R[n_, i_] := Union[Table[Mod[k(k-1), i], {k, 1, n}]]; Do[Do[If[Length[R[n, i]]==n, Print[n, " ", i]; Goto[aa]], {i, 1, 4n}]; Print[n]; Label[aa]; Continue, {n, 1, 1000}]
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CROSSREFS
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Cf. A000040, A207982, A208494.
Sequence in context: A066066 A241957 A112070 * A123252 A352185 A066168
Adjacent sequences: A208640 A208641 A208642 * A208644 A208645 A208646
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KEYWORD
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nonn
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AUTHOR
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Zhi-Wei Sun, Feb 29 2012
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STATUS
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approved
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