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

1,1

Comments

Conjecture: the sequence is infinite.

Links

Table of n, a(n) for n=1..36.

Example

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

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 *)

Prog

(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

Crossrefs

Intersection of A005574, A049422, A114270, A113536.

Subsequence of A182238.

Sequence in context: A012722 A012616 A012611 * A356175 A133757 A246164

Adjacent sequences: A356106 A356107 A356108 * A356110 A356111 A356112

Keyword

nonn

Author

Michel Lagneau, Jul 27 2022

Status

approved