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A005473
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Primes of form n^2 + 4.
(Formerly M3830)
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12
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5, 13, 29, 53, 173, 229, 293, 733, 1093, 1229, 1373, 2029, 2213, 3253, 4229, 4493, 5333, 7229, 7573, 9029, 9413, 10613, 13229, 13693, 15629, 18229, 18773, 21613, 24029, 26573, 27893, 31333, 33493, 37253, 41213, 42853, 46229, 47093, 54293
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) mod 24 = 5 or 13 and if a(n) mod 24 =13 then a(n) mod 72 = 13.
For n>=2 a(n)= A098062(n-1). - Zak Seidov, Apr 12 2007
Contribution from Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008: (Start)
Primes p such that continued fraction of (1+Sqrt[p])/2 has period 1.
Primes in A078370 = primes of the form 4 k^2 + 4 k + 5. (End)
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REFERENCES
| D. Shanks, The simplest cubic fields, Math. Comp., 28 (1974), 1137-1152.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..4600
Eric Weisstein's World of Mathematics, Near-Square Prime
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FORMULA
| a(n)=24*A056904(n)+m, where m=13 if A056904(n) is three times a triangular number (and n>0) and m=5 if A056904(n) is not three times a triangular number (or n=0).
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EXAMPLE
| a(2)=29 since 29=5^2+4 is prime.
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MATHEMATICA
| Intersection[Table[n^2+4, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=4, i<=4, 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
aa = {}; Do[If[PrimeQ[4 k^2 + 4 k + 5], AppendTo[aa, 4 k^2 + 4 k + 5]], {k, 0, 200}]; aa [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]
Select[Table[n^2+4, {n, 0, 7000}], PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)
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PROG
| (PARI) for(n=1, 1e3, if(isprime(t=n^2+4), print1(t", "))) \\ Charles R Greathouse IV, Jul 05 2011
(MAGMA) [a: n in [0..300] | IsPrime(a) where a is n^2+4]; // Vincenzo Librandi, Nov 30 2011
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CROSSREFS
| Subsequence of A185086.
a(n)-4 is contained in A016754. (a(n)-5)/8 is contained in A000217. Either (a(n)-5)/24 is contained in A001318 (if a(n) mod 24=5) or (a(n)-13)/72 is contained in A000217 (if a(n) mod 24=13). Floor[a(n)/24] is contained in A001840.
A146326 [From Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008]
Sequence in context: A130230 A106931 A078370 * A086732 A162329 A160430
Adjacent sequences: A005470 A005471 A005472 * A005474 A005475 A005476
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms and additional comments from Henry Bottomley (se16(AT)btinternet.com), Jul 06 2000
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