A347364 Primes of the form p^4 + p^2 - 1 where p is prime.

19, 89, 28729, 130681, 1875529, 3420649, 7893289, 112561489, 373320361, 777824209, 1506177289, 3262865761, 4362536449, 5887416169, 8882968249, 9355048561, 18141261409, 21517809409, 22898196361, 27983100241, 35152312609, 62001747001, 67123223641, 85662460441, 89526324889, 100469663929

Offset

1,1

Comments

a(n) == 1 (mod 72) for n >= 3. - Hugo Pfoertner, Aug 29 2021

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 28729 is a term because 28729 = 13^4 + 13^2 - 1, and 13 and 28729 are primes.

Maple

map(t -> t^4+t^2-1, select(t -> isprime(t) and isprime(t^4+t^2-1), [2, seq(i, i=3..10000, 2)]));

Mathematica

f[p_] := p^4 + p^2 - 1; Select[Map[f, Select[Range[600], PrimeQ]], PrimeQ] (* Amiram Eldar, Aug 29 2021 *)
Select[Table[p^4+p^2-1, {p, Prime[Range[200]]}], PrimeQ] (* Harvey P. Dale, Aug 11 2024 *)

Prog

(Python)
from sympy import isprime, primerange
def auptop(maxp): return list(filter(isprime, (p**4 + p**2 -1 for p in primerange(1, maxp+1))))
print(auptop(580)) # Michael S. Branicky, Aug 29 2021

Crossrefs

Sequence in context: A126406 A201306 A160296 * A224097 A088574 A096031

Adjacent sequences: A347361 A347362 A347363 * A347365 A347366 A347367

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 29 2021

Status

approved