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A051800 Numbers k such that 1 plus twice the product of the first k primes is also a prime.

%I A051800 #29 May 30 2023 08:27:00
%S A051800 1,2,3,4,5,11,18,23,26,30,80,120,148,220,395,776,884,977,3535,3927
%N A051800 Numbers k such that 1 plus twice the product of the first k primes is also a prime.
%e A051800 5 is in the sequence because 2*(2*3*5*7*11) + 1 = 4621 is prime.
%t A051800 Position[2#+1&/@FoldList[Times,Prime[Range[800]]],_?PrimeQ]//Flatten (* _Harvey P. Dale_, Oct 09 2018 *)
%o A051800 (PARI) isok(k) = isprime(1+2*prod(j=1, k, prime(j))); \\ _Michel Marcus_, May 28 2018
%o A051800 (Python)
%o A051800 from sympy import isprime, nextprime
%o A051800 def afind(limit):
%o A051800     p, primorialk = 2, 2
%o A051800     for k in range(1, limit+1):
%o A051800         if isprime(2*primorialk + 1):
%o A051800             print(k, end=", ")
%o A051800         p = nextprime(p)
%o A051800         primorialk *= p
%o A051800 afind(400) # _Michael S. Branicky_, Dec 24 2021
%Y A051800 2*A002110(n)+1 is prime. Cf. A051887, A051915.
%K A051800 nonn,more
%O A051800 1,2
%A A051800 _Labos Elemer_, Dec 20 1999
%E A051800 More terms from _Harvey P. Dale_, Oct 09 2018
%E A051800 a(17)-a(18) from _Michael S. Branicky_, Dec 24 2021
%E A051800 a(19)-a(20) from _Michael S. Branicky_, May 30 2023