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a(n) is the k-th upper twin prime, where k = n!.
1

%I #14 Jul 22 2024 10:19:16

%S 5,5,7,43,463,4639,51349,563011,6445993,80358601,1066687471,

%T 15116681443,228312888439

%N a(n) is the k-th upper twin prime, where k = n!.

%F From _Amiram Eldar_, Jul 07 2024: (Start)

%F a(n) = A006512(n!).

%F a(n) = A093310(n) + 2. (End)

%o (PARI)

%o twinu(n) = { local(c,x); c=0; x=1; while(c<n, if(isprime(prime(x)+2),c++); x++; ); return(prime(x)) }

%o g(n) = for(x=0,n,print1(twinu(x!),","))

%Y Cf. A006512, A093310.

%K nonn,more

%O 0,1

%A _Cino Hilliard_, Apr 25 2004

%E a(9)-a(12) from _Giovanni Resta_, Jun 10 2018