A177014 a(n) is the smallest number m such that all the n numbers 1!*m+1, 2!*m+1, ..., n!*m+1 are prime.
1, 1, 1, 18, 18, 8628, 748668, 2506980, 228698250, 228698250
Offset: 1
Examples
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. The corresponding primes are: n=1: 2; n=2: 2, 3; n=3: 2, 3, 7; n=4: 19, 37, 109, 433; n=5: 19, 37, 109, 433, 2161; n=6: 8629, 17257, 51769, 207073, 1035361, 6212161; n=7: 748669, 1497337, 4492009, 17968033, 89840161, 539040961, 3773286721; ...
Crossrefs
Cf. A177013.
Programs
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PARI
okm(m, n) = {for (k=1, n, if (! isprime(k!*m+1), return (0));); return (1);} a(n) = {m = 1; while(! okm(m, n), m++); m;} \\ Michel Marcus, Jun 08 2014
Extensions
a(10) corrected by Jon E. Schoenfield, Mar 07 2018