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Greatest common divisor of n^2 - 7 and n^2 + 7.
1

%I #20 Sep 08 2022 08:45:12

%S 7,2,1,2,1,2,1,14,1,2,1,2,1,2,7,2,1,2,1,2,1,14,1,2,1,2,1,2,7,2,1,2,1,

%T 2,1,14,1,2,1,2,1,2,7,2,1,2,1,2,1,14,1,2,1,2,1,2,7,2,1,2,1,2,1,14,1,2,

%U 1,2,1,2,7,2,1,2,1,2,1,14,1,2,1,2,1,2,7,2,1,2,1,2,1,14,1,2,1,2,1,2,7,2,1

%N Greatest common divisor of n^2 - 7 and n^2 + 7.

%C a(n) is the product of the periodic sequences [1,2]*[7,1,1,1,1,1,1]. - _Gary Detlefs_, Apr 22 2011

%H Vincenzo Librandi, <a href="/A089129/b089129.txt">Table of n, a(n) for n = 0..1000</a>

%F From _Gary Detlefs_, Apr 22 2011: (Start)

%F a(n) = gcd(n+7, 14).

%F a(n) = (6*(1-(n^6 mod 7))+1)*((n mod 2)+1). (End)

%o (PARI) g(n,k) = for(x=0,n,print1(gcd(x^k-7,x^k+7)","))

%o (Magma) [Gcd(n^2+7,n^2-7): n in [0..100] ]; // _Vincenzo Librandi_, Apr 22 2011

%K easy,nonn

%O 0,1

%A _Cino Hilliard_, Dec 05 2003