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

Author

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

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

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

Crossrefs

Contained in A106483 and A243595.

Programs

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 *)

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