

A091421


Numbers n such that n#*2^n  1 is prime, where n# is product of prime numbers (primorials).


1



1, 2, 3, 4, 6, 7, 8, 15, 19, 31, 68, 69, 78, 82, 162, 210, 524, 770, 1058, 1437, 1730, 3977
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OFFSET

1,2


COMMENTS

1# = 2 2# = 2*3 = 6 3# = 2*3*5 = 30.


LINKS



EXAMPLE

a(1)=1 because 1#*2^1  1 = 3 is prime.
a(2)=2 because 2#*2^2  1 = 23 is prime.


MATHEMATICA

For[n = 1, n < 60, n++, If[PrimeQ[2^n*Product[Prime[i], {i, 1, n}]  1], Print[n]]] (* Stefan Steinerberger, Feb 06 2006 *)


PROG

(PARI) pp(n)= s=1; for(i=1, n, s=s*prime(i)); return(s);
f(n)=pp(n)!*2^n 1;
for (i=1, 500, if(isprime(f(i)), print1(i, ", ")))


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004


EXTENSIONS



STATUS

approved



