A211173 - OEIS

%I #28 Mar 04 2024 01:14:42

%S 0,2,1,6,0,10,1,0,1,18,0,22,0,0,1,30,0,0,1,0,1,42,0,46,0,0,1,0,0,58,1,

%T 0,0,66,0,70,1,0,0,78,0,82,0,0,1,0,0,0,1,0,1,102,0,106,1,0,1,0,0,0,0,

%U 0,0,126,0,130,0,0,1,138,0

%N (2n)!^n (modulo 2n+1).

%C a(n)= 0, 1 or 2n. In fact, a(n) = 0 iff n belongs to A047845, a(n) = 1 iff n belongs to A104636 and a(n) = 2n iff n belongs to A104635.

%H Charles R Greathouse IV, <a href="/A211173/b211173.txt">Table of n, a(n) for n = 0..10000</a>

%H Larry Riddle, <a href="http://www.agnesscott.edu/lriddle/women/germain-flt/sgandflt.htm"> Sophie Germain and Fermat's Last Theorem</a>, Agnes Scott College, Math. Dept. Jul, 1999.

%F a(n) = (2n)!^n (modulo 2n+1).

%t f[n_] := Mod[((2 n)!)^n, 2 n + 1]; Array[f, 70]

%t Table[PowerMod[(2n)!,n,2n+1],{n,0,70}] (* _Harvey P. Dale_, Nov 02 2019 *)

%o (PARI) a(n)=if(isprime(2*n+1),if(n%2,2*n,1),0) \\ _Charles R Greathouse IV_, Feb 07 2013

%Y Cf. A047845, A104635, A104636.

%K nonn,easy

%O 0,2

%A Larry Riddle (LRiddle(AT)AgnesScott.edu) and _Robert G. Wilson v_, Jan 31 2013