Original entry on oeis.org
109, 433, 172801, 238573, 363313, 640333, 1145773, 1968301, 2056753, 3121201, 3577393, 6588973, 11197873, 13079233, 13381633, 15431473, 21676033, 26462701, 34476301, 37340353, 43823053, 48481201, 54749953, 56454733, 90816013, 96038893, 102667501, 128786113
Offset: 1
172801 is a term because 172801 = (241^3 - 239^3)/2, and 172801, 239 and 241 are all primes.
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from itertools import islice
from sympy import isprime, nextprime
def A360490_gen(): # generator of terms
p, q = 3**3, 5
while True:
if isprime(k:=(m:=q**3)-p>>1):
yield k
p, q = m, nextprime(q)
A360490_list = list(islice(A360490_gen(),20)) # Chai Wah Wu, Feb 27 2023
A237627
Semiprimes of the form n^3 + n^2 + n + 1.
Original entry on oeis.org
4, 15, 85, 259, 1111, 4369, 47989, 65641, 291919, 2016379, 2214031, 3397651, 3820909, 5864581, 9305311, 13881841, 15687751, 16843009, 19756171, 22030681, 28746559, 62256349, 64160401, 74264821, 79692331, 101412319, 117889591, 172189309, 185518471, 191435329
Offset: 1
85 is in the sequence since 4^3 + 4^2 + 4 + 1 = 85 = 5 * 17, which is a semiprime.
259 is in the sequence since 6^3 + 6^2 + 6 + 1 = 259 = 7 * 37 which is a semiprime.
585 is not in the sequence, because, although it is 8^3 + 8^2 + 8 + 1, it has more than two prime factors.
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IsSemiprime:=func; [s: n in [1..1000] | IsSemiprime(s) where s is n^3+n^2+n+1]; // Bruno Berselli, Apr 23 2014
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select(x-> numtheory[bigomega](x)=2, [n^3+n^2+n+1$n=1..1500])[];
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A237627 = {}; Do[t = n^3 + n^2 + n + 1; If[PrimeOmega[t] == 2, AppendTo[A237627, t]], {n, 1500}]; A237627 (* K. D. Bajpai *)
(* For the b-file: *) n = 0; Do[t = k^3 + k^2 + k + 1; If[PrimeOmega[t] == 2, n++; Print[n, " ", t]], {k, 300000}] (* K. D. Bajpai *)
Select[Table[n^3 + n^2 + n + 1, {n, 500}], PrimeOmega[#] == 2 &] (* Alonso del Arte, Apr 22 2014 *)
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is(n)=isprime(n^2+1) && isprime(n+1) \\ Charles R Greathouse IV, Aug 25 2014
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from itertools import islice
from sympy import isprime, nextprime
def A237627_gen(): # generator of terms
p = 1
while (p:=nextprime(p)):
if isprime((p-1)**2+1):
yield p*((p-1)**2+1)
A237627_list = list(islice(A237627_gen(),20)) # Chai Wah Wu, Feb 27 2023
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A237627 = list(n^3 + n^2 + n + 1 for n in (1..1000) if is_prime(n^2+1) and is_prime(n+1)); print(A237627) # Bruno Berselli, Apr 23 2014 - see comment by Alonso del Arte
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