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A049423
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Primes of the form n^2+3.
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11
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Note that all terms after the first are equal to 7 modulo 12
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Near-Square Prime
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FORMULA
| Primes m such that m-3 is a square
For n>0, a(n)=36*A056902(n-1)^2+24*A056902(n-1)+7. - Henry Bottomley (se16(AT)btinternet.com), Jul 06 2000
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EXAMPLE
| a(2)=4^2+3=19 which is prime
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MATHEMATICA
| 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 Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008
Select[Table[n^2+3, {n, 0, 198000}], PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)
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PROG
| (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
| 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.
Sequence in context: A148669 A160128 A051139 * A121825 A066237 A135741
Adjacent sequences: A049420 A049421 A049422 * A049424 A049425 A049426
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Jobling (paul.jobling(AT)whitecross.com)
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