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%I #26 Jan 30 2020 08:09:16
%S 2,3,7,5,7,41,283,3,127,11161,1427,17,8011,821,607,2161,4903,509,1607,
%T 127,11261,8273,12037,58207,419,11491,2153,1789,9059,67843,29,5641,
%U 1999,2459,1699,15299,35747,2531,10987,26497,36781,719,24709,13721,29803,1049
%N Smallest prime q such that 2*prime(n)*q^prime(n)+1 is also prime.
%H Pierre CAMI, <a href="/A225403/b225403.txt">Table of n, a(n) for n = 1..250</a>
%e 2*2*2^2+1 = 17 prime so a(1) = 2,
%e 2*3*2^3+1 = 49 composite,
%e 2*3*3^3+1 = 163 prime so a(2) = 3,
%e 2*5*2^5+1 = 321 composite,
%e 2*5*3^5+1 = 2431 composite,
%e 2*5*5^5+1 = 31251 composite,
%e 2*5*7^5+1 = 168071 prime so a(3) = 7.
%o (PFGW & SCRIPTIFY)
%o SCRIPT
%o DIM n,0
%o DIM k
%o DIM q
%o DIM pp
%o DIMS t
%o OPENFILEOUT myfile,a(n).txt
%o LABEL a
%o SET n,n+1
%o IF n>250 THEN END
%o SET k,0
%o LABEL b
%o SET k,k+1
%o SET q,p(k)
%o SETS t,%d,%d\,;n;q
%o SET pp,2*p(n)*q^p(n)+1
%o PRP pp,t
%o IF ISPRP THEN GOTO c
%o GOTO b
%o LABEL c
%o WRITE myfile,t
%o GOTO a
%o (PARI) a(n) = my(q=2); while(!isprime(2*prime(n)*q^prime(n)+1), q = nextprime(q+1)); q; \\ _Michel Marcus_, Sep 23 2019
%K nonn
%O 1,1
%A _Pierre CAMI_, May 13 2013