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Search: id:A162876
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| A162876 |
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Twin prime pairs p, p+2 such that p-1 and p+3 are both square-free. |
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1
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| 3, 5, 11, 13, 59, 61, 71, 73, 107, 109, 179, 181, 191, 193, 227, 229, 311, 313, 419, 421, 431, 433, 599, 601, 659, 661, 827, 829, 1019, 1021, 1031, 1033, 1091, 1093, 1319, 1321, 1427, 1429, 1487, 1489, 1607, 1609, 1619, 1621, 1787, 1789, 1871, 1873, 1931
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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By definition, the lower member, here at the odd indexed positions, is in A089188.
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FORMULA
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{(p,p+2) : p in A001359, and p-1 in A005117, and p+3 in A005117}.
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EXAMPLE
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(179,181) are in the sequence because 179-1=2*89 is square-free and 181+1=2*7*13 is also square-free.
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MATHEMATICA
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f[n_]:=Module[{a=m=0}, Do[If[FactorInteger[n][[m, 2]]>1, a=1], {m, Length[FactorInteger[n]]}]; a]; lst={}; Do[p=Prime[n]; r=p+2; If[PrimeQ[r], If[f[p-1]==0&&f[r+1]==0, AppendTo[lst, p]; AppendTo[lst, r]]], {n, 7!}]; lst
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CROSSREFS
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Cf. A089194, A097375, A162870, A162872, A162873, A162874, A162875
Sequence in context: A006794 A032457 A122564 this_sequence A162875 A166564 A058595
Adjacent sequences: A162873 A162874 A162875 this_sequence A162877 A162878 A162879
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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), Jul 15 2009
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EXTENSIONS
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Definition rephrased by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 27 2009
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