A356510 Primes p such that 2*p^2 - 7, 2*p^2 - 1, and 2*p^2 + 3 are prime.

43, 127, 197, 3613, 3767, 4957, 28687, 29723, 40193, 46817, 66403, 78737, 89137, 93253, 104243, 105337, 105673, 110543, 114113, 123397, 127247, 145963, 148303, 168713, 173293, 190387, 201893, 207367, 213613, 241597, 256117, 261323, 268253, 278543, 283807, 333227, 339373, 340913, 356173, 359143

Offset

1,1

Comments

All terms == 3 or 7 (mod 10).

All terms == 1 or 13 (mod 14). - Jon E. Schoenfield, Sep 05 2022

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(3) = 197 is a term because 197, 2*197^2 - 7 = 77611, 2*197^2 - 1 = 77617, and 2*197^2 + 3 = 77621 are all prime.

Maple

filter:= p -> isprime(p) and isprime(2*p^2+3) and isprime(2*p^2-1) and isprime(2*p^2-7):
select(filter, [seq(i, i=3..1000000, 2)]);

Mathematica

Select[Prime[Range[30000]], AllTrue[2*#^2 + {-7, -1, 3}, PrimeQ] &] (* Amiram Eldar, Aug 09 2022 *)

Prog

(Python)
from sympy import isprime
def ok(n): return isprime(n) and all(isprime(2*n*n-i) for i in [7, 1, -3])
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Aug 09 2022

Crossrefs

Contained in A106483 and A243595.

Sequence in context: A044294 A044675 A112270 * A124826 A136069 A140028

Adjacent sequences: A356507 A356508 A356509 * A356511 A356512 A356513

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 09 2022

Status

approved