%I #29 Sep 08 2022 08:45:05
%S 1,4,2,4,6,2,2,2,2,6,16,2,6,4,6,6,20,2,4,6,2,2,4,2,2,6,4,12,2,6,2,12,
%T 6,2,50,8,2,4,2,2,2,14,12,2,2,40,4,56,6,2,18,30,2,18,86,2,10,2,2,6,2,
%U 6,2,24,2,6,2,2,4,10,6,36,8,22,4,6,6,2,6,2,6,2,24,2,2,2,2,2,6,2,156,6,2,4
%N a(n) = gcd(prime(2*n)+1, prime(n)+1).
%C Starting with a(2)=4, all terms are even. - _Zak Seidov_, Jul 16 2016
%H Harry J. Smith and Michael De Vlieger, <a href="/A066978/b066978.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%e a(4) = gcd(prime(8) + 1, prime(4) + 1) = gcd(19 + 1, 7 + 1) = gcd(20, 8) = 4.
%t Table[GCD[Prime[2 n] + 1, Prime@ n + 1], {n, 92}] (* _Michael De Vlieger_, Dec 03 2015 *)
%o (PARI) { for (n=1, 1000, write("b066978.txt", n, " ", gcd(prime(2*n) + 1, prime(n) + 1)) ) } \\ _Harry J. Smith_, Apr 13 2010
%o (Magma) [Gcd(NthPrime(2*n)+1, NthPrime(n)+1): n in [1..80]]; // _Vincenzo Librandi_, Dec 04 2015
%Y Cf. A097009 (gcd(prime(2*n) - 1, prime(n) - 1)).
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jan 26 2002