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A180475
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Primes of the form p^5 + p^3 + 1 where p is a prime.
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1
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41, 271, 3251, 1424771, 6448511, 115925123, 229448831, 18425794691, 38581737743, 48264295811, 73443083699, 996266439503, 1258302388991, 1752012093443, 2159450038451, 2909420102783, 3201110256371, 18248780996099, 32198944966271, 124287677598479, 142214634995891
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OFFSET
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1,1
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LINKS
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Michael S. Branicky, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) ~ prime(n)^18.
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EXAMPLE
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115925123 is a term since 41^5 + 41^3 + 1 = 115925123 is prime.
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MATHEMATICA
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Select[ #^5 + #^3 + 1 & /@ Prime@ Range@ 90, PrimeQ] (* Robert G. Wilson v, Sep 10 2010 *)
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PROG
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(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
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CROSSREFS
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Cf. A000040, A180474.
Sequence in context: A020866 A142690 A089318 * A142768 A140013 A342299
Adjacent sequences: A180472 A180473 A180474 * A180476 A180477 A180478
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KEYWORD
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nonn
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AUTHOR
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Carmine Suriano, Sep 07 2010
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EXTENSIONS
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a(19) and beyond from Michael S. Branicky, Mar 12 2022
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STATUS
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approved
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