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

%I #23 Aug 31 2024 04:33:33

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

%T 3977,5104,8440

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

%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, A091424.

%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

%E a(23)-a(24) from _Michael S. Branicky_, Aug 28 2024