A256519 - OEIS

%I #16 Apr 04 2015 19:14:55

%S 25,121,169,437,551,667,721,1037,1159,1273,1349,1403,1541,1769,1943,

%T 2209,2329,2363,2419,3071,3713,4087,5041,5111,7313,8357,8479,9017,

%U 11357,11983,12673,16117,16343,19043,19099,19879

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

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

%H Charles R Greathouse IV, <a href="/A256519/b256519.txt">Table of n, a(n) for n = 1..719</a>

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

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

%o (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

%K nonn

%O 1,1

%A _Felix Fröhlich_, Apr 01 2015

%E a(25)-a(36) from _Charles R Greathouse IV_, Apr 02 2015