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A333390 Numbers k such that (2*k)# * 2^k - 1 is prime.

%I A333390 #28 Jun 26 2024 19:46:38
%S A333390 1,2,3,4,5,12,17,22,26,28,30,50,120,186,215,246,323,1021,1160,1404,
%T A333390 1431,1461,1786,2317,2960,4484,4613,5192,5345,6518,6865,9951,14493,
%U A333390 14798,16653,17372
%N A333390 Numbers k such that (2*k)# * 2^k - 1 is prime.
%C A333390 No more terms < 6700.
%C A333390 No more terms < 10^4. - _Daniel Suteu_, Mar 20 2020
%o A333390 (Python)
%o A333390 from sympy.ntheory.generate import primorial, isprime
%o A333390 A333390_list = [n for n in range(1,100) if isprime(primorial(2*n,nth=False)*2**n-1)] # _Chai Wah Wu_, Mar 18 2020
%o A333390 (PARI) is(k) = ispseudoprime(lcm(primes([2, 2*k]))*2^k-1); \\ _Jinyuan Wang_, Mar 20 2020
%Y A333390 Cf. A034386 (n#), A084406.
%K A333390 nonn,hard,more
%O A333390 1,2
%A A333390 _L. Joris Perrenet_, Mar 18 2020
%E A333390 a(31) from _Jinyuan Wang_, Mar 20 2020
%E A333390 a(32) from _Daniel Suteu_, Mar 20 2020
%E A333390 a(33)-a(36) from _Michael S. Branicky_, Jun 26 2024