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A112723
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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.
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3
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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