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

%I #23 Aug 31 2024 04:34:08

%S 1,3,4,6,10,30,31,98,156,230,432,490,1623,1666,9324,9693

%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 = 5 is prime

%e a(2) = 3 because 3#*2^3 + 1 = 241 is prime

%o (PARI) pp(n)=my(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, A091421.

%K nonn,hard,more

%O 1,2

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

%E a(13)-a(14) from _Chai Wah Wu_, Dec 23 2019

%E a(15)-a(16) from _Michael S. Branicky_, Aug 31 2024