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%I #17 Mar 12 2022 18:08:52
%S 41,271,3251,1424771,6448511,115925123,229448831,18425794691,
%T 38581737743,48264295811,73443083699,996266439503,1258302388991,
%U 1752012093443,2159450038451,2909420102783,3201110256371,18248780996099,32198944966271,124287677598479,142214634995891
%N Primes of the form p^5 + p^3 + 1 where p is a prime.
%H Michael S. Branicky, <a href="/A180475/b180475.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ prime(n)^18.
%e 115925123 is a term since 41^5 + 41^3 + 1 = 115925123 is prime.
%t Select[ #^5 + #^3 + 1 & /@ Prime@ Range@ 90, PrimeQ] (* _Robert G. Wilson v_, Sep 10 2010 *)
%o (Python)
%o from itertools import islice
%o from sympy import isprime, nextprime
%o def agen(): # generator of terms
%o p = 2
%o while True:
%o t = p**5 + p**3 + 1
%o if isprime(t):
%o yield t
%o p = nextprime(p)
%o print(list(islice(agen(), 21))) # _Michael S. Branicky_, Mar 12 2022
%Y Cf. A000040, A180474.
%K nonn
%O 1,1
%A _Carmine Suriano_, Sep 07 2010
%E a(19) and beyond from _Michael S. Branicky_, Mar 12 2022
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