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%I #14 Feb 29 2020 03:18:42
%S 121,703,1729,1891,2821,7381,8401,8911,10585,12403,15457,15841,16531,
%T 18721,19345,23521,24661,28009,29341,31621,41041,44287,46657,47197,
%U 49141,50881,52633,55969,63139,63973,74593,75361,79003,82513,87913,88573,93961,97567,105163
%N Composite numbers k such that (1 - w)^(k-1) == 1 (mod k) in the ring of Eisenstein integers (w = (-1 + sqrt(3)*i)/2).
%C w = exp(2*Pi*i/3) = (-1 + sqrt(3)*i)/2), where i is the imaginary unit, is a unit in the ring of Eisenstein integers (usually denoted by the Greek letter omega).
%C Also Euler-Jacobi pseudoprimes to base 3 that are congruent to 1 (mod 6).
%H Amiram Eldar, <a href="/A329705/b329705.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weissteins's World of Mathematics, <a href="http://mathworld.wolfram.com/EisensteinInteger.html">Eisenstein Integer</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Eisenstein_integer">Eisenstein integer</a>.
%t eisProd[z1_, z2_] := {z1[[1]]*z2[[1]] - z1[[2]]*z2[[2]], z1[[1]]*z2[[2]] + z1[[2]]*z2[[1]] - z1[[2]]*z2[[2]]}; seq = {}; z = {1, 0}; Do[z = eisProd[{1, -1}, z]; If[CompositeQ[n] && And @@ Divisible[z - {1, 0}, n], AppendTo[seq, n]], {n, 2, 10^4}]; seq
%Y Intersection of A016921 and A048950.
%Y Cf. A066408, A270698.
%K nonn
%O 1,1
%A _Amiram Eldar_, Feb 28 2020
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