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%I #13 Mar 17 2020 17:42:29
%S 1,2,3,4,6,7,8,15,19,31,68,69,78,82,162,210,524,770,1058,1437,1730,
%T 3977
%N Numbers n such that n#*2^n - 1 is prime, where n# is product of prime numbers (primorials).
%C 1# = 2 2# = 2*3 = 6 3# = 2*3*5 = 30.
%C No more terms < 5000. - _L. Joris Perrenet_, Mar 17 2020
%e a(1)=1 because 1#*2^1 - 1 = 3 is prime.
%e a(2)=2 because 2#*2^2 - 1 = 23 is prime.
%t For[n = 1, n < 60, n++, If[PrimeQ[2^n*Product[Prime[i], {i, 1, n}] - 1], Print[n]]] (* _Stefan Steinerberger_, Feb 06 2006 *)
%o (PARI) pp(n)= s=1; for(i=1,n,s=s*prime(i)); return(s);
%o f(n)=pp(n)!*2^n -1;
%o for (i=1,500,if(isprime(f(i)),print1(i, ", ")))
%Y Cf. A002110.
%K nonn,hard,more
%O 1,2
%A Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004
%E a(17) from _Stefan Steinerberger_, Feb 06 2006
%E a(18)-a(22) from _L. Joris Perrenet_, Mar 17 2020
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