A347364 - OEIS

%I #18 Aug 11 2024 15:31:28

%S 19,89,28729,130681,1875529,3420649,7893289,112561489,373320361,

%T 777824209,1506177289,3262865761,4362536449,5887416169,8882968249,

%U 9355048561,18141261409,21517809409,22898196361,27983100241,35152312609,62001747001,67123223641,85662460441,89526324889,100469663929

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

%C a(n) == 1 (mod 72) for n >= 3. - _Hugo Pfoertner_, Aug 29 2021

%H Robert Israel, <a href="/A347364/b347364.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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)]));

%t f[p_] := p^4 + p^2 - 1; Select[Map[f, Select[Range[600], PrimeQ]], PrimeQ] (* _Amiram Eldar_, Aug 29 2021 *)

%t Select[Table[p^4+p^2-1,{p,Prime[Range[200]]}],PrimeQ] (* _Harvey P. Dale_, Aug 11 2024 *)

%o (Python)

%o from sympy import isprime, primerange

%o def auptop(maxp): return list(filter(isprime, (p**4 + p**2 -1 for p in primerange(1, maxp+1))))

%o print(auptop(580)) # _Michael S. Branicky_, Aug 29 2021

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Aug 29 2021