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A117847 Numbers k such that A060256(k)*prime(k)# - 1 is a Sophie Germain prime, where prime(k)# is the k-th primorial. 0

%I #13 Sep 11 2021 10:47:47

%S 1,2,3,4,8,9,10,15,24,35,37,79,340

%N Numbers k such that A060256(k)*prime(k)# - 1 is a Sophie Germain prime, where prime(k)# is the k-th primorial.

%C This sequence gives the firsts of twin primes (A060256(n)*prime(n)# - 1, A060256(n)*prime(n)# + 1) which are also Sophie Germain primes.

%C a(14) > 367. - _Amiram Eldar_, Sep 11 2021

%e 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.

%t 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 *)

%Y Cf. A002110, A005384, A060256.

%K nonn,hard,more

%O 1,2

%A _Pierre CAMI_, May 01 2006

%E a(1)-a(6) inserted by _Amiram Eldar_, Sep 11 2021

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)