A309844 Primes of the form n^4 + n^2 + 3.

3, 5, 23, 653, 10103, 83813, 160403, 234743, 280373, 1049603, 3420653, 6252503, 11319863, 52207853, 92246423, 146422103, 174913853, 221548343, 442071653, 479807123, 577224653, 607597853, 655385603, 937921253, 1222865933, 1249233683, 1387525253, 1506177293

Offset

1,1

Comments

Digital root of all values > 3 is 5, compare A017221.

Links

Table of n, a(n) for n=1..28.

Mathematica

f[n_] := n^4 + n^2 + 3; Select[f /@ Range[0, 200], PrimeQ] (* Amiram Eldar, Aug 24 2019 *)

Prog

(MATLAB)
a = [];
for n = 0:1e3
    x = n.^4+n.^2+3;
    if isprime(x); a = [a, x]; end;
end
(Python)
from sympy import isprime
a = []
for n in range(0, 1000):
    x = n**4+n**2+3
    if isprime(x):
        a.append(x)

Crossrefs

Subset of A027753. Subset of A017221.

Cf. A037896, A182344, A182345, A049423.

Sequence in context: A137087 A214589 A365036 * A062218 A050280 A005761

Adjacent sequences: A309841 A309842 A309843 * A309845 A309846 A309847

Keyword

nonn,easy

Author

Christopher R. Madan, Aug 19 2019

Status

approved