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A329916 Smallest k such that 6*k*A057130(n)-1 and 6*k*A057130(n)+1 are twin primes.

%I A329916 #29 Dec 06 2019 18:03:52
%S A329916 1,2,3,23,11,18,77,46,84,76,22,30,3,107,26,198,136,23,236,284,167,269,
%T A329916 381,405,379,374,620,481,606,505,163,1414,348,639,1696,1429,850,2050,
%U A329916 740,117,362,35,3961,72,1307,1816,9410,5705,972,368,5083,4387,3296,6039
%N A329916 Smallest k such that 6*k*A057130(n)-1 and 6*k*A057130(n)+1 are twin primes.
%C A329916 A057130 gives the product of prime numbers (-1 mod 6) in the order of occurrence.
%e A329916 A057130(1)=5, 6*1*5-1=29, and 29 and 31 are twin primes, so a(1)=1.
%e A329916 A057130(2)=55, 6*2*55-1=659, and 659 and 661 are twin primes, so a(2)=2.
%o A329916 (PFGW Script)
%o A329916 SCRIPT
%o A329916 DIM i,0
%o A329916 DIM j
%o A329916 DIM k
%o A329916 DIM n,1
%o A329916 OPENFILEOUT myf,a(n).txt
%o A329916 OPENFILEIN maf,a007528.txt
%o A329916 LABEL a
%o A329916 SET i,i+1
%o A329916 IF i>100 THEN END
%o A329916 GETNEXT j,maf
%o A329916 SET n,n*j
%o A329916 SET k,0
%o A329916 LABEL b
%o A329916 SET k,k+1
%o A329916 PRP k*6+1,k
%o A329916 IF ISPRP THEN GOTO c
%o A329916 GOTO b
%o A329916 LABEL c
%o A329916 PRP k*6*n-1,k
%o A329916 IF ISPRP THEN GOTO d
%o A329916 GOTO b
%o A329916 LABEL d
%o A329916 WRITE myf,k
%o A329916 GOTO a
%o A329916 (PARI) lista(nn) = {my(pp = 1); forprime (p = 1, nn, if (Mod(p, 6) == -1, pp *= p; my(k=1); while (!isprime(6*k*pp-1) || !isprime(6*k*pp+1), k++); print1(k, ", ");););} \\ _Michel Marcus_, Nov 25 2019
%Y A329916 Cf. A001359, A006512, A007528, A057130, A060256, A173937, A329736.
%K A329916 nonn
%O A329916 1,2
%A A329916 _Pierre CAMI_, Nov 24 2019