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%I #42 Nov 08 2024 07:14:44
%S 2,3,25,721,3628801,479001601,20922789888001,6402373705728001,
%T 1124000727777607680001,304888344611713860501504000001,
%U 265252859812191058636308480000001,371993326789901217467999448150835200000001
%N a(n) = (prime(n) - 1)! + 1.
%C If the prime p is in A055469, that is if p = 2, 7, 11, 29, ... = A055469(j) which is valid for the first, 4th, 5th, 10th,.... entry here with j = 1, 2, 3, ..., then a(n) = A052295[A067186(j)] + 1. - _R. J. Mathar_, Apr 27 2007
%C It follows from Wilson's theorem that a(n) is divisible by the n-th prime. - _Alonso del Arte_, Feb 07 2014
%H Harry J. Smith, <a href="/A060371/b060371.txt">Table of n, a(n) for n = 1..88</a> (adapted by Vincenzo Librandi, Oct 17 2017)
%H Takashi Agoh, Karl Dilcher and Ladislav Skula, <a href="https://doi.org/10.1090/S0025-5718-98-00951-X">Wilson quotients for composite moduli</a>, Math. Comp. 67 (1998), 843-861. MR 98h:11003.
%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=WilsonPrime">Wilson Primes</a>
%H R. Crandall, K. Dilcher and C. Pomerance, <a href="http://dx.doi.org/10.1090/S0025-5718-97-00791-6">A search for Wieferich and Wilson primes</a>, Math. Comp., 66 (1997), 433-449. MR 97c:11004.
%t Table[(Prime[n] - 1)! + 1, {n, 12}] (* _Alonso del Arte_, Feb 07 2014 *)
%o (PARI) { n=1; forprime (p=1, 524, write("b060371.txt", n++, " ", (p - 1)! + 1); ) } \\ _Harry J. Smith_, Jul 04 2009
%o (Magma) [Factorial(NthPrime(n)-1)+1: n in [1..15]]; // _Vincenzo Librandi_, Oct 17 2017
%Y Cf. A052295, A055469, A067186.
%Y Subsequence of A038507. - _Michel Marcus_, Oct 17 2017
%K nonn
%O 1,1
%A _Jason Earls_, Apr 01 2001
%E Corrected offset by _Alonso del Arte_, Feb 07 2014