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A236056 Numbers k such that k^2 +- k +- 1 is prime for all four possibilities. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The only prime in this sequence is a(1) = 3.
LINKS
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
KEYWORD
nonn
AUTHOR
Derek Orr, Jan 18 2014
STATUS
approved

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Last modified July 14 02:38 EDT 2024. Contains 374291 sequences. (Running on oeis4.)