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A180475
Primes of the form p^5 + p^3 + 1 where p is a prime.
1
41, 271, 3251, 1424771, 6448511, 115925123, 229448831, 18425794691, 38581737743, 48264295811, 73443083699, 996266439503, 1258302388991, 1752012093443, 2159450038451, 2909420102783, 3201110256371, 18248780996099, 32198944966271, 124287677598479, 142214634995891
OFFSET
1,1
LINKS
FORMULA
a(n) ~ prime(n)^18.
EXAMPLE
115925123 is a term since 41^5 + 41^3 + 1 = 115925123 is prime.
MATHEMATICA
Select[ #^5 + #^3 + 1 & /@ Prime@ Range@ 90, PrimeQ] (* Robert G. Wilson v, Sep 10 2010 *)
PROG
(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
p = 2
while True:
t = p**5 + p**3 + 1
if isprime(t):
yield t
p = nextprime(p)
print(list(islice(agen(), 21))) # Michael S. Branicky, Mar 12 2022
CROSSREFS
Sequence in context: A020866 A142690 A089318 * A142768 A140013 A342299
KEYWORD
nonn
AUTHOR
Carmine Suriano, Sep 07 2010
EXTENSIONS
a(19) and beyond from Michael S. Branicky, Mar 12 2022
STATUS
approved