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A049423
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Primes of the form k^2 + 3.
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13
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3, 7, 19, 67, 103, 199, 487, 787, 1447, 2503, 2707, 3847, 4099, 4903, 5479, 5779, 8467, 8839, 11239, 12547, 14887, 16903, 17959, 19603, 21319, 23719, 24967, 25603, 29587, 31687, 47527, 52903, 58567, 59539, 61507, 65539, 75079, 81799, 88807
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OFFSET
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1,1
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COMMENTS
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Note that all terms after the first are congruent to 7 modulo 12.
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LINKS
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FORMULA
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Primes m such that m-3 is a square.
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EXAMPLE
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19 is prime and is equal to 4^2 + 3, so 19 is a term.
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MATHEMATICA
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Intersection[Table[n^2+3, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=3, i<=3, a={}; Do[If[PrimeQ[n^2+i], AppendTo[a, n^2+i]], {n, 0, 100}]; Print["n^2+", i, ", ", a]; i++ ] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
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PROG
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(Magma) [n: n in PrimesUpTo(175000) | IsSquare(n-3)]; // Bruno Berselli, Apr 05 2011
(Magma) [a: n in [0..300] | IsPrime(a) where a is n^2+3]; // Vincenzo Librandi, Dec 08 2011
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CROSSREFS
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Cf. A002496, A056899. Note that apart from first term, all of (a(n)-7)/12 have to be terms of A001082 for a(n) to be prime.
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Jobling (paul.jobling(AT)whitecross.com)
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STATUS
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approved
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