A236766 Numbers n such that n^4 +/- n +/- 1 are prime for all four possibilities.

6, 9, 7266, 115131, 380529, 536646, 636609, 818526, 922734, 1389015, 1660119, 2045415, 2085726, 2262420, 2469396, 2722260, 2836374, 2954250, 3146904, 3614226, 3949770, 4062465, 4110834, 4211499, 4400100, 5081055, 5324424, 5434794, 5436090

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

380529^4+380529+1 (20967711831335262645811), 380529^4+380529-1 (20967711831335262645809), 380529^4-380529+1 (20967711831335261884753), and 380529^4-380529-1 (20967711831335261884751) are all prime. Thus, 380529 is a member of this sequence.

Mathematica

Select[Range[55*10^5], AllTrue[#^4+{(#-1), (#+1), (-#-1), (-#+1)}, PrimeQ]&] (* Harvey P. Dale, Nov 02 2024 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(n) for n in range(10**7) if isprime(n**4+n+1) and isprime(n**4-n+1) and isprime(n**4+n-1) and isprime(n**4-n-1)}
(PARI)
for(n=1, 5000000, if(isprime(n^4+n+1)&&isprime(n^4-n+1)&&isprime(n^4+n-1)&&isprime(n^4-n-1), print1(n, ", "))) \\ Colin Barker, Jan 31 2014

Crossrefs

Intersection of A236759, A049408, A236761 and A126424.

Sequence in context: A061110 A110460 A159190 * A004075 A202951 A316633

Adjacent sequences: A236763 A236764 A236765 * A236767 A236768 A236769

Keyword

nonn

Author

Derek Orr, Jan 30 2014

Status

approved