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%I #17 Dec 18 2017 03:00:44
%S 3,7,13,7,31,43,19,73,13,37,19,157,61,211,241,307,127,421,463,79,601,
%T 31,37,757,271,67,331,151,1123,397,97,43,67,1483,223,547,1723,139,631,
%U 283,109,103,61,181,2551,379,919,409,2971,79,103,3307,163,3541,523,97,3907
%N Primes that appear in the sequence p:=x^2+x+1, sieved with a quadratic sieve construction.
%C This sequence appears in a website available on web.archive (see Quadratic Sieve Construction link). There is a single appearance of the first term 3, while all other primes appear twice. See A256148 for a version of the sequence consistent with the current version of the website where each prime appears only once. - _Ray Chandler_, Jul 05 2015
%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>.
%H Bernhard Helmes, <a href="http://web.archive.org/web/20050407001733/http://www.devalco.de/quadratisches_Siebverfahren.htm">Quadratic Sieve Construction</a> (web.archive).
%o (MuPAD) // from Quadratic Sieve Construction link.
%o liste_max:=10000;
%o for x from 1 to liste_max do
%o liste_x[x]:=x^2+x+1;
%o liste_prim[x]:=1;
%o end_for;
%o x:=1;
%o while (x<liste_max) do
%o stelle:=x;
%o p:=liste_x[x];
%o if (p>1) then
%o print ("Prim ", p, "x = ", x, isprime (p)) ;
%o // Aussiebung
%o while (stelle<liste_max) do
%o erg:=liste_x[stelle];
%o while (erg mod p = 0) do
%o erg:=erg /p;
%o end_while;
%o liste_x[stelle]:=erg;
%o liste_prim[stelle]:=0;
%o // print ("x= ",stelle, erg, p);
%o stelle:=stelle+p;
%o end_while;
%o end_if;
%o x:=x+1;
%o end_while;
%o // _Ray Chandler_, Jul 05 2015
%Y Cf. A002061, A002383, A007645, A162471, A256148.
%K nonn,uned,obsc
%O 1,1
%A Bernhard Helmes (pi(AT)devalco.de), Jun 24 2005
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