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%I #35 Sep 08 2022 08:46:14
%S 0,0,3,56,511,194,46976,104633,546681,41130177,643108140,7034542959,
%T 65748733699,1518781632657,35097481516962,396029533782911,
%U 4146710666095789,159899356955923308,3662069108121609141,109629928744379590001,828180977946159463007
%N a(n) = prime(n)! mod prime(n!).
%C Inspired by A261997.
%C a(n) = n and a(n) = prime(n-1) for n=3.
%C a(n) = 0 only for n=1 and n=2. What is the minimum value of a(n) for n > 2? Is there a possibility of observing that a(n) = 1 or a(n) = 2?
%F a(n) = A039716(n) mod A062439(n).
%e a(1) = prime(1)! mod prime(1!) = 2 mod 2 = 0.
%e a(2) = prime(2)! mod prime(2!) = 6 mod 3 = 0.
%e a(3) = prime(3)! mod prime(3!) = 120 mod 13 = 3.
%t Table[Mod[Prime[n]!, Prime[n!]], {n, 15}] (* _Michael De Vlieger_, Sep 21 2015 *)
%o (PARI) a(n) = prime(n)! % prime(n!);
%o vector(11, n, a(n))
%o (Magma) [Factorial(NthPrime(n)) mod NthPrime(Factorial(n)): n in [1..11]]; // _Vincenzo Librandi_, Sep 23 2015
%Y Cf. A000040, A039716, A062439, A261997.
%K nonn
%O 1,3
%A _Altug Alkan_, Sep 21 2015
%E a(11)-a(15) from _Michael De Vlieger_, Sep 21 2015
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