A364701 - OEIS

%I #27 Mar 05 2024 16:46:54

%S 1531398,114009582,940084647,4206644978,7962908038,20293639091,

%T 41947594698

%N Pseudoprimes corresponding to a Perrin-like primality test.

%C 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).

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

%H Robert Dougherty-Bliss and Doron Zeilberger, <a href="https://arxiv.org/abs/2307.16069v1">Lots and Lots of Perrin-Type Primality Tests and Their Pseudo-Primes</a>, arXiv:2307.16069 [math.NT], 2023.

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

%Y b(n) is A362923.

%Y Cf. A001608, A013998, A018187.

%K nonn,more

%O 1,1

%A _Robert Dougherty-Bliss_, Aug 03 2023