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

1,1

Comments

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

Links

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

Example

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

Prog

(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

Crossrefs

Sequence in context: A083509 A343075 A339130 * A298009 A213445 A363190

Adjacent sequences: A256516 A256517 A256518 * A256520 A256521 A256522

Keyword

nonn

Author

Felix Fröhlich, Apr 01 2015

Extensions

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

Status

approved