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A103579
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Sophie Germain primes that are not Lucasian primes.
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0
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2, 5, 29, 41, 53, 89, 113, 173, 233, 281, 293, 509, 593, 641, 653, 761, 809, 953, 1013, 1049, 1229, 1289, 1409, 1481, 1601, 1733, 1889, 1901, 1973, 2069, 2129, 2141, 2273, 2393, 2549, 2693, 2741, 2753
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sophie Germain primes A005384 are those primes p such that 2p+1 is also prime. Lucasian primes A002515 are those primes p such that p == 3 (mod 4) with 2p+1 prime.
Sophie Germain primes that are also hypotenuses of primitive Pythagorean triangles. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 07 2009]
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FORMULA
| Primes p such that 2p+1 is prime and not p == 3 (mod 4). {A005384} - {A002515}. 2 Union {primes p such that 2p+1 is prime and p == 1 (mod 4). 2 Union {A002145 Intersection A005384}.
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MATHEMATICA
| f[n_]:=Module[{k=1}, While[(n-k^2)^(1/2)!=IntegerPart[(n-k^2)^(1/2)], k++; If[2*k^2>=n, k=0; Break[]]]; k]; lst1={}; Do[If[f[n^2]>0, a=f[n^2]; b=(n^2-a^2)^(1/2); If[GCD[n, a, b]==1, If[PrimeQ[n]&&PrimeQ[2*n+1], AppendTo[lst1, n]]]], {n, 3, 4*6!}]; lst1 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 07 2009]
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CROSSREFS
| Cf. A002145, A002515, A005384.
Sequence in context: A165161 A098858 A134449 * A161500 A061351 A126107
Adjacent sequences: A103576 A103577 A103578 * A103580 A103581 A103582
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 23 2005
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EXTENSIONS
| Mathematica and more terms from Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 07 2009
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