A236056 Numbers k such that k^2 +- k +- 1 is prime for all four possibilities.

3, 6, 21, 456, 1365, 2205, 2451, 2730, 8541, 18486, 32199, 32319, 32781, 45864, 61215, 72555, 72561, 82146, 83259, 86604, 91371, 95199, 125334, 149331, 176889, 182910, 185535, 210846, 225666, 226254, 288420, 343161, 350091, 403941, 411501, 510399, 567204

Offset

1,1

Comments

The only prime in this sequence is a(1) = 3.

Links

Table of n, a(n) for n=1..37.

Example

1365^2 + 1365 + 1 = 1864591,
1365^2 + 1365 - 1 = 1864589,
1365^2 - 1365 + 1 = 1861861, and
1365^2 - 1365 - 1 = 1861859 are all prime, so 1365 is a term of this sequence.

Maple

q:= k-> andmap(isprime, [seq(seq(k^2+i+j, j=[k, -k]), i=[1, -1])]):
select(q, [3*t$t=1..200000])[];  # Alois P. Heinz, Feb 25 2020

Mathematica

Select[Range[568000], AllTrue[Flatten[{#^2+#+{1, -1}, #^2-#+{1, -1}}, 1], PrimeQ]&] (* Harvey P. Dale, Jul 31 2022 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(p) for p in range(10**6) if isprime(p**2+p+1) and isprime(p**2-p+1) and isprime(p**2+p-1) and isprime(p**2-p-1)}

Crossrefs

Numbers in the intersection of A002384, A045546, A055494, and A002328.

Numbers in the intersection of A131530 and A088485.

Sequence in context: A019054 A066986 A096662 * A347616 A280116 A295578

Adjacent sequences: A236053 A236054 A236055 * A236057 A236058 A236059

Keyword

nonn

Author

Derek Orr, Jan 18 2014

Status

approved