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%I #12 Apr 17 2017 05:23:42
%S 2,6,30,420,2587200,6787314293760,52056502538040,
%T 8086849458453393732601350665011200000000
%N a(n) is the smallest number m such that the first n primes is the set of all distinct prime divisors of m and for i=1, 2,...,n prime(i)*m-1 is prime.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_334.htm">The Prime Puzzles & Problems connection</a>.
%e a(6) = 6787314293760 because {2,3,5,7,11,13} = {prime(1),prime(2),..., prime(6)} is the set of prime factors of 6787314293760, all six numbers 2*6787314293760-1,3*6787314293760-1, 5*6787314293760-1,7*6787314293760-1,11*6787314293760-1 & 13*6787314293760-1 are prime and 6787314293760 is the first number with such properties.
%t a[n_] := Block[{p = Prime@Range@n, stp, k}, stp = k = Times @@ p; While[First /@ FactorInteger[k] != p || ! AllTrue[p k - 1, PrimeQ], k += stp]; k]; Array[a, 5] (* _Giovanni Resta_, Apr 17 2017 *)
%Y Cf. A092023, A092024, A112724.
%K hard,nonn
%O 1,1
%A _Farideh Firoozbakht_, Nov 05 2005
%E a(7)-a(8) from _Giovanni Resta_, Apr 14 2017
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