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The prime(n)-th upper twin prime.
1

%I #12 Sep 12 2024 16:34:59

%S 7,13,31,61,139,181,241,283,433,643,811,1033,1153,1279,1429,1669,1933,

%T 1999,2143,2341,2551,2791,3121,3361,3583,3853,3931,4093,4159,4261,

%U 5011,5281,5641,5659,6361,6553,6781,7129,7351,7759,8233,8389,9013,9241,9433

%N The prime(n)-th upper twin prime.

%F a(n) = A006512(A000040(n)). - _Andrew Howroyd_, Sep 12 2024

%e The first prime is 2. The 2nd upper twin prime is 7, which gives the first entry.

%t With[{twprs=Transpose[Select[Partition[Prime[Range[10000]],2,1], Last[#]- First[#] == 2&]][[2]]},Flatten[Table[Take[twprs,{Prime[n]}],{n,50}]]] (* _Harvey P. Dale_, Jul 25 2011 *)

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

%o a(n) = twinu(prime(n))

%Y Cf. A000040, A006512.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, May 17 2007