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A163512
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Primes of the form (1 + k + k^3)/3.
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2
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23, 337, 2293, 3557, 9941, 21347, 39233, 87403, 251221, 333367, 895253, 1080647, 1217473, 1696207, 2076563, 2626933, 2999707, 4493837, 6203297, 6857033, 8045953, 8299127, 8821297, 11442817, 13807361, 14538187, 17298497, 21333467
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OFFSET
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1,1
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COMMENTS
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k must be congruent to 1 (mod 3) for (k^3 + k + 1)/3 to be an integer. - Michael B. Porter, Apr 07 2010
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LINKS
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EXAMPLE
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(1 + 4 + 4^3)/3 = 23.
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MATHEMATICA
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f[n_]:=(1+n+n^3)/3; lst={}; Do[If[PrimeQ[f[n]], AppendTo[lst, f[n]]], {n, 7!}]; lst
Select[Table[(n^3+n+1)/3, {n, 400}], PrimeQ] (* Harvey P. Dale, Aug 28 2012 *)
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PROG
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(PARI) for(n=0, 200, m=3*n+1; if(isprime((m^3+m+1)/3), print((m^3+m+1)/3))) \\ Michael B. Porter, Apr 07 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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