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A355188
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Primes p such that (2^p+p^2)/3 is prime.
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0
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5, 7, 17, 43, 61, 73, 241, 739, 1297, 4211, 98519
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OFFSET
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1,1
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COMMENTS
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No more terms < 50000.
Intersection with A242929 (primes p such that 2^p-p^2 is prime) includes 5, 7 and 17. Any others?
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LINKS
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EXAMPLE
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a(3) = 17 is a term because (2^17+17^2)/3 = 43787 is prime.
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MAPLE
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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
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Select[Prime[Range[600]], PrimeQ[(2^# + #^2)/3] &] (* Amiram Eldar, Jun 23 2022 *)
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PROG
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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
(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)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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