A356109 Numbers k such that k^2 + {1,3,7,13} are prime.

2, 4, 10, 5996, 8894, 11204, 14290, 23110, 30866, 37594, 43054, 64390, 74554, 83464, 93460, 109456, 111940, 132304, 151904, 184706, 238850, 262630, 265990, 277630, 300206, 315410, 352600, 355450, 376190, 404954, 415180, 462830, 483494, 512354, 512704, 566296

Offset: 1

Author

Michel Lagneau, Jul 27 2022

Keywords

• nonn

Comments

Conjecture: the sequence is infinite.

Examples

			2^2 + {1,3,7,13} = {5,7,11,17} all prime.
4^2 + {1,3,7,13} = {17,19,23,29} all prime.
		

Crossrefs

Intersection of A005574, A049422, A114270, A113536.

Subsequence of A182238.

Programs

Maple

q:= k-> andmap(j-> isprime(k^2+j), [1,3,7,13]):
select(q, [$0..1000000])[];  # Alois P. Heinz, Jul 27 2022

Mathematica

Select[Range[500000], AllTrue[#^2 + {1,3,7,13}, PrimeQ] &] (* Amiram Eldar, Jul 27 2022 *)

Python

from sympy import isprime
def ok(n): return all(isprime(n*n+i) for i in {1,3,7,13})
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 27 2022