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Primitive prime factors of the cyclotomic polynomial sequence Phi(3, k) (or Phi(6, k)) in the order in which they occur.
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%I #23 Oct 13 2022 18:47:28

%S 3,7,13,31,43,19,73,37,157,61,211,241,307,127,421,463,79,601,757,271,

%T 67,331,151,1123,397,97,1483,223,547,1723,139,631,283,109,103,181,

%U 2551,379,919,409,2971,3307,163,3541,523,3907,613,4423,4831,1657,5113,751

%N Primitive prime factors of the cyclotomic polynomial sequence Phi(3, k) (or Phi(6, k)) in the order in which they occur.

%C Phi(3,k) = k^2 + k + 1 and Phi(6,k) = k^2 - k + 1.

%C Interesting scatter plot.

%C The terms correspond to the new primes of A081257 in the order of their appearance for n>1 and when A081257(m)>m. - _Bill McEachen_, Oct 13 2022

%H Robert Price, <a href="/A256148/b256148.txt">Table of n, a(n) for n = 1..733</a>

%H Bernhard Helmes, <a href="http://www.devalco.de/quadr_Sieb_x%5E2+x+1.php">Prime sieving on the polynomial f(n)=n^2+n+1</a>.

%t prim = {}; Do[prim = Join[prim, Complement[First /@ FactorInteger[Cyclotomic[6, k]], prim]], {k, 1000}]; prim

%o (PARI) lista(nn) = {vs = []; for (n=1, nn, vp = factor(polcyclo(6,n))[,1]; for (i=1, #vp, if (!vecsearch(vs, vp[i]), print1(vp[i], ", "); vs = vecsort(concat(vs, vp[i]),,8););););} \\ _Michel Marcus_, Mar 20 2015

%Y Cf. A005529, A248874, A256144, A256145, A256146, A081257.

%K nonn,look

%O 1,1

%A _Robert Price_, Mar 16 2015