A256519 Composites c for which an integer 1 < k < c exists such that (c-k)! == -1 (mod c).

25, 121, 169, 437, 551, 667, 721, 1037, 1159, 1273, 1349, 1403, 1541, 1769, 1943, 2209, 2329, 2363, 2419, 3071, 3713, 4087, 5041, 5111, 7313, 8357, 8479, 9017, 11357, 11983, 12673, 16117, 16343, 19043, 19099, 19879

Offset: 1

Author

Felix Fröhlich, Apr 01 2015

Keywords

• nonn

Comments

The 1 < k part of the condition in the definition is implied by Wilson's theorem.

Examples

			c = 25 satisfies the congruence with k = 21, since ((25-21)!+1) mod 25 = 0, so 25 is a term of the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..719

Programs

PARI

forcomposite(c=1, , for(k=1, c-1, if(Mod((c-k)!, c)==-1, print1(c, ", "); break({1}))))

PARI

is(n)=if(isprime(n), return(0)); my(m=Mod(6,n)); for(k=4,n,m*=k; if(m==-1, return(1));if(gcd(m,n)!=1,return(0))) \\ Charles R Greathouse IV, Apr 02 2015

Extensions

a(25)-a(36) from Charles R Greathouse IV, Apr 02 2015