A091421 Numbers m such that m#*2^m - 1 is prime, where m# = A002110(m).

1, 2, 3, 4, 6, 7, 8, 15, 19, 31, 68, 69, 78, 82, 162, 210, 524, 770, 1058, 1437, 1730, 3977, 5104, 8440

Offset: 1

Author

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

Keywords

• nonn
• hard
• more

Comments

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

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

Examples

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

Crossrefs

Cf. A002110, A091424.

Programs

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 *)

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, ", ")))

Extensions

a(17) from Stefan Steinerberger, Feb 06 2006

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

a(23)-a(24) from Michael S. Branicky, Aug 28 2024