A236072 Numbers n such that n^4 + n + 1 and n^4 - n - 1 are prime.

2, 5, 6, 9, 11, 26, 44, 60, 77, 147, 239, 384, 545, 690, 770, 779, 1071, 1127, 1190, 1271, 1296, 1331, 1506, 1659, 1707, 1871, 1880, 1986, 2037, 2442, 2520, 2541, 2714, 2960, 2982, 3045, 3060, 3110, 3189, 3287, 3464, 3609

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

384^4 + 384 + 1 and 384^4 - 384 - 1 are both prime, so 384 is a member of this sequence.

Mathematica

Select[Range[4000], AllTrue[#^4+{#+1, -#-1}, PrimeQ]&] (* Harvey P. Dale, Jan 20 2025 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p**4-p-1) and isprime(p**4+p+1)}
(PARI)
s=[]; for(n=1, 4000, if(isprime(n^4+n+1) && isprime(n^4-n-1), s=concat(s, n))); s \\ Colin Barker, Jan 19 2014

Crossrefs

Numbers in both A126424 and A049408.

Sequence in context: A286341 A284657 A230506 * A055938 A190764 A276886

Adjacent sequences: A236069 A236070 A236071 * A236073 A236074 A236075

Keyword

nonn

Author

Derek Orr, Jan 19 2014

Status

approved