OFFSET
1,1
COMMENTS
Primes p such that p^2-1 is not in A355643.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2) = 3 is a term because it is prime, the divisors of 3^2-1 = 8 are 1, 2, 4 and 8, and none of 1+8/1 = 9, 2+8/2 = 6, 4+8/4 = 6, 8+8/8 = 9 are prime.
MAPLE
filter:= proc(p) local n, F, t;
n:= p^2-1;
F:= select(t -> t^2 <=n, numtheory:-divisors(n));
not ormap(isprime, map(t -> t+n/t, F))
end proc:
select(filter, [seq(ithprime(i), i=1..3000)]);
MATHEMATICA
q[n_] := AllTrue[Divisors[n], !PrimeQ[# + n/#] &]; Select[Prime[Range[2000]], q[#^2 - 1] &] (* Amiram Eldar, Jul 11 2022 *)
PROG
(PARI) isok(p) = isprime(p) && fordiv(p^2-1, d, if (isprime(d + (p^2-1)/d), return(0))); return(1); \\ Michel Marcus, Jul 11 2022
(Python)
from sympy import divisors, isprime
def ok(n):
if not isprime(n): return False
t = n**2 - 1
return not any(isprime(d+t//d) for d in divisors(t, generator=True))
print([k for k in range(19000) if ok(k)]) # Michael S. Branicky, Jul 11 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 11 2022
STATUS
approved