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A208643 Least positive integer m such that those k*(k-1) mod m with k=1,...,n are pairwise distinct.

%I A208643 #22 Sep 10 2018 13:53:22
%S A208643 1,3,5,7,11,11,13,16,17,19,23,23,29,29,29,31,37,37,37,41,41,43,47,47,
%T A208643 53,53,53,59,59,59,61,64,67,67,71,71,73,79,79,79,83,83,89,89,89,97,97,
%U A208643 97,97,101,101,103,107,107,109,113,113,127,127,127
%N A208643 Least positive integer m such that those k*(k-1) mod m with k=1,...,n are pairwise distinct.
%C A208643 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,....
%H A208643 Zhi-Wei Sun, <a href="/A208643/b208643.txt">Table of n, a(n) for n = 1..500</a>
%H A208643 Zhi-Wei Sun, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;df748f41.1202">A function taking only prime values</a>, a message to Number Theory List, Feb. 21, 2012.
%H A208643 Zhi-Wei Sun, <a href="http://dx.doi.org/10.1016/j.jnt.2013.02.003">On functions taking only prime values</a>, J. Number Theory 133(2013), no.8, 2794-2812.
%t A208643 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}]
%Y A208643 Cf. A000040, A207982, A208494.
%K A208643 nonn
%O A208643 1,2
%A A208643 _Zhi-Wei Sun_, Feb 29 2012