A364701 Pseudoprimes corresponding to a Perrin-like primality test.

1531398, 114009582, 940084647, 4206644978, 7962908038, 20293639091, 41947594698

Offset: 1

Author

Robert Dougherty-Bliss, Aug 03 2023

Keywords

• nonn
• more

Comments

The sequence b(n) defined by the generating function (3*x^4+5*x^2+6*x-7)/(4*x^7+x^4+x^2+x-1) has the property that b(p) == 1 (mod p) if p is a prime. A pseudoprime for b(n) is a composite number k such that b(k) == 1 (mod k).

The first seven pseudoprimes are the only ones up to 10^12.

Examples

			The value of b(1531398) is a 399290-digit number which is congruent to 1 modulo 1531398 = 2 * 3 * 11 * 23203.
		

Links

• Robert Dougherty-Bliss and Doron Zeilberger, Lots and Lots of Perrin-Type Primality Tests and Their Pseudo-Primes, arXiv:2307.16069 [math.NT], 2023.

Crossrefs

b(n) is A362923.

Cf. A001608, A013998, A018187.