A091421 Numbers n such that n#*2^n - 1 is prime, where n# is product of prime numbers (primorials).

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

Offset

1,2

Comments

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

No more terms < 5000. - L. Joris Perrenet, Mar 17 2020

Links

Table of n, a(n) for n=1..22.

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

Cf. A002110.

Sequence in context: A096360 A039087 A093710 * A138936 A135604 A345437

Adjacent sequences: A091418 A091419 A091420 * A091422 A091423 A091424

Keyword

nonn,hard,more

Author

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

Extensions

a(17) from Stefan Steinerberger, Feb 06 2006

a(18)-a(22) from L. Joris Perrenet, Mar 17 2020

Status

approved