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
Examples
a(3) = 17 is a term because (2^17+17^2)/3 = 43787 is prime.
Crossrefs
Cf. A242929.
Programs
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Maple
filter:= proc(p) isprime(p) and isprime((2^p+p^2)/3) end proc: select(filter, [seq(i,i=5..10000,2)]);
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Mathematica
Select[Prime[Range[600]], PrimeQ[(2^# + #^2)/3] &] (* Amiram Eldar, Jun 23 2022 *)
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PARI
isok(p) = if (isprime(p), my(q=(2^p+p^2)/3); (denominator(q)==1) && ispseudoprime(q)); \\ Michel Marcus, Jun 23 2022
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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
Extensions
a(11) from Daniel Suteu, Jun 25 2022
Comments