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 A208643 Least positive integer m such that those k*(k-1) mod m with k=1,...,n are pairwise distinct. 13
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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,.... LINKS 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. MATHEMATICA 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}] CROSSREFS Cf. A000040, A207982, A208494. Sequence in context: A066066 A241957 A112070 * A123252 A352185 A066168 Adjacent sequences: A208640 A208641 A208642 * A208644 A208645 A208646 KEYWORD nonn AUTHOR Zhi-Wei Sun, Feb 29 2012 STATUS approved

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Last modified March 28 15:08 EDT 2023. Contains 361595 sequences. (Running on oeis4.)