A356110 Numbers k such that k^2 + {1,3,7,13,31} are prime.

4, 10, 14290, 43054, 109456, 315410, 352600, 483494, 566296, 685114, 927070, 1106116, 1248796, 1501174, 1997986, 2399204, 2501404, 2553100, 2726840, 2874680, 3291760, 4129394, 4473766, 4794520, 4901144, 6350306, 7444070, 7753456, 7892504, 8009536, 8069540

Offset: 1

Author

Michel Lagneau, Jul 27 2022

Keywords

• nonn

Comments

Conjecture: the sequence is infinite.

Examples

			4^2 + {1,3,7,13,31} = {17,19,23,29,47} are all prime.
		

Crossrefs

Cf. A005574, A049422, A114270, A113536, A182238, A356109.

Programs

Maple

q:= k-> andmap(j-> isprime(k^2+j), [1,3,7,13,31]):
select(q, [$0..1000000])[];  # Alois P. Heinz, Jul 27 2022

Mathematica

Select[Range[10^6], AllTrue[#^2 + {1,3,7,13,31}, PrimeQ] &] (* Amiram Eldar, Jul 27 2022 *)

Python

from sympy import isprime
def ok(n): return all(isprime(n*n+i) for i in {1,3,7,13,31})
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 27 2022