A355188 Primes p such that (2^p+p^2)/3 is prime.

5, 7, 17, 43, 61, 73, 241, 739, 1297, 4211, 98519

Offset

1,1

Comments

Intersection with A242929 (primes p such that 2^p-p^2 is prime) includes 5, 7 and 17. Any others?

a(12) > 4*10^5. - Michael S. Branicky, Oct 31 2024

Links

Table of n, a(n) for n=1..11.

Example

a(3) = 17 is a term because (2^17+17^2)/3 = 43787 is prime.

Maple

filter:= proc(p) isprime(p) and isprime((2^p+p^2)/3) end proc:
select(filter, [seq(i, i=5..10000, 2)]);

Mathematica

Select[Prime[Range[600]], PrimeQ[(2^# + #^2)/3] &] (* Amiram Eldar, Jun 23 2022 *)

Prog

(PARI) isok(p) = if (isprime(p), my(q=(2^p+p^2)/3); (denominator(q)==1) && ispseudoprime(q)); \\ Michel Marcus, Jun 23 2022
(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen():
    p = 2
    while True:
        t = 2**p+p**2
        if t%3 == 0 and isprime(t//3):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 10))) # Michael S. Branicky, Jun 23 2022

Crossrefs

Cf. A242929.

Sequence in context: A113282 A323200 A096741 * A106955 A030785 A019404

Adjacent sequences: A355185 A355186 A355187 * A355189 A355190 A355191

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Jun 23 2022

Extensions

a(11) from Daniel Suteu, Jun 25 2022

Status

approved