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%I #9 Sep 11 2021 10:48:00
%S 1,7,8,13,26,58
%N Numbers k such that A103557(k)*((prime(k)#)^2) - 1 is a Sophie Germain prime, where prime(k)# is the k-th primorial.
%C a(7) > 200. - _Amiram Eldar_, Sep 11 2021
%t q[n_] := Module[{p2 = Product[Prime[i], {i,1,n}]^2, k=1}, While[!PrimeQ[k*p2-1] || !PrimeQ[k*p2+1], k++]; PrimeQ[2*k*p2 - 1]]; Select[Range[100], q] (* _Amiram Eldar_, Sep 11 2021 *)
%Y Cf. A002110, A005384, A103557.
%K nonn,hard,more
%O 1,2
%A _Pierre CAMI_, May 11 2006
%E Data corrected by _Amiram Eldar_, Sep 11 2021