A004055 - OEIS

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

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OFFSET

1,2

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]

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 *)

PROG

(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

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

CROSSREFS

Cf. A058302, A065091.

Sequence in context: A073662 A086553 A342068 * A077933 A144762 A141572

Adjacent sequences: A004052 A004053 A004054 * A004056 A004057 A004058

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Dec 11 1996

STATUS

approved