A364701 Pseudoprimes corresponding to a Perrin-like primality test.

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

Offset

1,1

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.

Links

Table of n, a(n) for n=1..7.

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

Example

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

Crossrefs

b(n) is A362923.

Cf. A001608, A013998, A018187.

Sequence in context: A236154 A126252 A268305 * A236117 A255694 A366890

Adjacent sequences: A364698 A364699 A364700 * A364702 A364703 A364704

Keyword

nonn,more

Author

Robert Dougherty-Bliss, Aug 03 2023

Status

approved