A177014 - OEIS

%I #11 Mar 09 2018 12:13:33

%S 1,1,1,18,18,8628,748668,2506980,228698250,228698250

%N a(n) is the smallest number m such that all the n numbers 1!*m+1, 2!*m+1, ..., n!*m+1 are prime.

%e a(5)=18 because each of the five numbers 1!*18+1, 2!*18+1, 3!*18+1, 4!*18+1 and 5!*18+1 is prime, and 18 is the smallest such number.

%e The corresponding primes are:

%e n=1:  2;

%e n=2:  2, 3;

%e n=3:  2, 3, 7;

%e n=4:  19, 37, 109, 433;

%e n=5:  19, 37, 109, 433, 2161;

%e n=6:  8629, 17257, 51769, 207073, 1035361, 6212161;

%e n=7:  748669, 1497337, 4492009, 17968033, 89840161, 539040961, 3773286721;

%e   ...

%o (PARI) okm(m, n) = {for (k=1, n, if (! isprime(k!*m+1), return (0));); return (1);}

%o a(n) = {m = 1; while(! okm(m, n), m++); m;} \\ _Michel Marcus_, Jun 08 2014

%Y Cf. A177013.

%K more,nonn

%O 1,4

%A _Enoch Haga_ and _Farideh Firoozbakht_, May 20 2010

%E a(10) corrected by _Jon E. Schoenfield_, Mar 07 2018