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Search: id:A153209
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| A153209 |
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Primes of the form 2*p+1 where p is prime and p+1 is square-free. |
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7
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| 5, 11, 59, 83, 227, 347, 563, 1019, 1283, 1307, 1523, 2459, 2579, 2819, 2963, 3803, 3947, 4259, 4547, 5387, 5483, 6779, 6827, 7187, 8147, 9587, 10667, 10883, 11003, 12107, 12227, 12539, 12659, 13043, 13163, 14243, 14387, 15683, 16139, 16187
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Subsequence of A005385.
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EXAMPLE
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For p = 2 (the only case with p+1 odd), 2*p+1 = 5 is prime and p+1 = 3 is square-free, so 5 is in the sequence. For p = 3, 2*p+1 = 7 is prime and p+1 = 4 is not square-free, so 7 is not in the sequence.
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MATHEMATICA
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<< NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n]; If[PrimeQ[Floor[p/2]]&&SquareFreeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
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PROGRAM
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(MAGMA) [ q: p in PrimesUpTo(8100) | IsSquarefree(p+1) and IsPrime(q) where q is 2*p+1 ];
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CROSSREFS
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Cf. A005117 (square-free numbers), A005385 (safe primes p: (p-1)/2 is also prime), A153207, A153208, A153210.
Sequence in context: A070198 A121934 A153812 this_sequence A106257 A104358 A104359
Adjacent sequences: A153206 A153207 A153208 this_sequence A153210 A153211 A153212
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 20 2008
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EXTENSIONS
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Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 24 2008
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