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

1,1

Comments

Conjecture: the sequence is infinite.

Links

Table of n, a(n) for n=1..31.

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A152396 A326720 A307491 * A048873 A091390 A321967

Adjacent sequences: A356107 A356108 A356109 * A356111 A356112 A356113

Keyword

nonn

Author

Michel Lagneau, Jul 27 2022

Status

approved