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 A177013 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

%I #13 Mar 07 2018 06:48:13

%S 3,3,3,3,3,1500,1500,154770,1656252,3240034842

%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)=3 because all five numbers 1!*3-1, 2!*3-1, 3!*3-1, 4!*3-1 and 5!*3-1 are prime and 3 is the smallest such number.

%e The corresponding primes are:

%e n=1: 2;

%e n=2: 2, 5;

%e n=3: 2, 5, 17;

%e n=4: 2, 5, 17, 71;

%e n=5: 2, 5, 17, 71, 359;

%e n=6: 1499, 2999, 8999, 35999, 179999, 1079999;

%e n=7: 1499, 2999, 8999, 35999, 179999, 1079999, 7559999;

%e n=8: 154769, 309539, 928619, 3714479, 18572399, 111434399, 780040799, 6240326399;

%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. A177014.

%K more,nonn

%O 1,1

%A _Enoch Haga_ and _Farideh Firoozbakht_, May 20 2010

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