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Search: id:A049423
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| A049423 |
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Primes of the form n^2+3. |
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+0
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; listen)
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OFFSET
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1,1
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COMMENT
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Note that all terms after the first are equal to 7 modulo 12
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LINKS
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Eric Weisstein's World of Mathematics, Near-Square Prime
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FORMULA
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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
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a(2)=4^2+3=19 which is prime
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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 Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008
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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.
Sequence in context: A071716 A005506 A051139 this_sequence A066237 A135741 A128024
Adjacent sequences: A049420 A049421 A049422 this_sequence A049424 A049425 A049426
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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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