
COMMENTS

The pseudoprimes derived from the fifthorder linear recurrence A225984(n) are analogous to the Perrin pseudoprimes A013998, and the Lucas pseudoprimes A005845.
For prime p, A225984(p) == p  1 (mod p). The pseudoprimes are composite numbers satisfying the same relation. 4 = 2^2; 14791044 = 2^2 * 3 * 19 * 29 * 2237; 143014853 = 907 * 157679.


PROG

(PARI)
N=10^10;
default(primelimit, N);
M = [0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, 0, 1, 1, 1];
a(n)=lift( trace( Mod(M, n)^n ) );
ta(n)=lift( trace( Mod(M, n) ) );
{ for (n=2, N,
if ( isprime(n), next() );
if ( a(n)==ta(n), print1(n, ", "); );
); }
/* Matt McIrvin, after Joerg Arndt's program for A013998, May 23 2013 */
