A004055 ((p-1)/2)! mod p for odd primes p.

1, 2, 6, 10, 5, 13, 18, 1, 12, 1, 31, 9, 42, 46, 23, 1, 11, 66, 1, 27, 78, 1, 34, 22, 91, 102, 1, 33, 15, 126, 130, 37, 1, 44, 1, 129, 162, 1, 80, 178, 162, 190, 81, 183, 198, 1, 1, 226, 122, 144, 1, 64, 1, 16, 262, 187, 1, 217, 53, 1, 138, 1, 1, 288, 114, 1, 189

Offset: 1

Author

Jeffrey Shallit, Dec 11 1996

Keywords

• nonn

Comments

Values 1 correspond to primes listed in A058302. - Max Alekseyev, Oct 24 2023

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..9999 [b-file corrected by _N. J. A. Sloane_, Oct 04 2010]

Crossrefs

Cf. A058302, A065091.

Programs

Magma

[Factorial((p-1) div 2) mod p: p in PrimesInInterval(3,350)]; // Vincenzo Librandi, May 01 2016

Maple

a:= n-> (p-> ((p-1)/2)! mod p)(ithprime(n+1)):
seq(a(n), n=1..73);  # Alois P. Heinz, Oct 25 2023

Mathematica

Mod[((#-1)/2)!, #]& /@ Prime[Range[2, 100]] (* Jean-François Alcover, Jan 02 2025 *)

PARI

lista(n)=forprime(p=3, n, print1(((p-1)/2)! % p, ", ")); \\ Michel Marcus, May 24 2013

PARI

a(n,p=prime(n+1))=lift(prod(k=2,p\2,k,Mod(1,p))) \\ Charles R Greathouse IV, May 01 2016