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A356510
Primes p such that 2*p^2 - 7, 2*p^2 - 1, and 2*p^2 + 3 are prime.
1
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Aug 09 2022
STATUS
approved