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A049407
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Numbers m such that m^3 + m + 1 is prime.
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39
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1, 2, 3, 5, 6, 8, 9, 12, 15, 17, 18, 21, 29, 30, 32, 39, 41, 42, 44, 48, 53, 54, 56, 60, 69, 71, 74, 77, 83, 87, 95, 102, 104, 108, 116, 117, 120, 126, 131, 135, 143, 144, 146, 152, 153, 155, 162, 168, 177, 179, 180, 186, 191, 207, 212, 219, 221, 225, 239, 240, 243
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OFFSET
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1,2
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COMMENTS
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For s = 5, 8, 11, 14, 17, 20, ... (A016789(s) for s>=2), m_s = 1 + m + m^s is composite for m>1. Also for m=1, m_s = 3 is a prime for any s. Here we consider the case s=3.
If m == 1 (mod 3), m_s == 0 (mod 3) for any s and is not prime for m > 1. Thus for n > 1, a(n) !== 1 (mod 3) and this is true for any similar sequence based on another s value (A002384, A049408, A075723). - Jean-Christophe Hervé, Sep 20 2014
Corresponding primes are in A095692.
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LINKS
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EXAMPLE
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3 is a term because 1 + 3 + 3^3 = 31 is a prime.
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MAPLE
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MATHEMATICA
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Select[Range[500], PrimeQ[Total[#^Range[1, 3, 2]] + 1] &] (* Vincenzo Librandi, Jun 27 2014 *)
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PROG
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(Magma) [n: n in [0..300] | IsPrime(s) where s is 1+&+[n^i: i in [1..3 by 2]]]; // Vincenzo Librandi, Jun 27 2014
(Python)
from sympy import isprime
def ok(m): return isprime(m**3 + m + 1)
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CROSSREFS
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Cf. A095692 (corresponding primes).
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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