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A117847
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Numbers k such that A060256(k)*prime(k)# - 1 is a Sophie Germain prime, where prime(k)# is the k-th primorial.
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0
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1, 2, 3, 4, 8, 9, 10, 15, 24, 35, 37, 79, 340
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OFFSET
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1,2
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COMMENTS
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This sequence gives the firsts of twin primes (A060256(n)*prime(n)# - 1, A060256(n)*prime(n)# + 1) which are also Sophie Germain primes.
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LINKS
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EXAMPLE
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16*(29#)-1 is the first of twin primes, 16 = A060256(10), 2*(16*(29#)-1)+1 is prime so 16*(29#)-1 is a Sophie Germain prime.
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MATHEMATICA
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q[n_] := Module[{p = Product[Prime[i], {i, 1, n}], k=1}, While[!PrimeQ[k*p-1] || !PrimeQ[k*p+1], k++]; PrimeQ[2*k*p - 1]]; Select[Range[100], q] (* Amiram Eldar, Sep 11 2021 *)
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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