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Search: id:A153208
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| A153208 |
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Primes of the form 2*p-1 where p is prime and p-1 is not square-free. |
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7
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| 37, 73, 193, 313, 397, 457, 541, 613, 673, 757, 1153, 1201, 1321, 1453, 1621, 1657, 1753, 1873, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2857, 2917, 3061, 3217, 3313, 4057, 4177, 4273, 4357, 4441, 4561, 4933, 5077, 5101, 5113, 5233, 5437, 5581, 5701
(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 A005383.
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EXAMPLE
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For p = 2 (the only case with p-1 odd), 2*p-1 = 3 is prime but p-1 = 1 is square-free, so 3 is not in the sequence. For p = 19, 2*p-1 = 37 is prime and p-1 = 18 is not square-free, so 37 is in the sequence.
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MATHEMATICA
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<< NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n]; If[ !SquareFreeQ[Floor[p/2]]&&PrimeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
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PROGRAM
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(MAGMA) [ q: p in PrimesUpTo(2900) | not IsSquarefree(p-1) and IsPrime(q) where q is 2*p-1 ];
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CROSSREFS
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Cf. A013929 (not square-free numbers), A005383 (numbers n such that both n and (n+1)/2 are primes), A153207, A153209, A153210.
Sequence in context: A043243 A044023 A069204 this_sequence A128388 A137833 A083748
Adjacent sequences: A153205 A153206 A153207 this_sequence A153209 A153210 A153211
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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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