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A153210
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Primes of the form 2*p+1 where p is prime and p+1 is not squarefree.
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6
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7, 23, 47, 107, 167, 179, 263, 359, 383, 467, 479, 503, 587, 719, 839, 863, 887, 983, 1187, 1319, 1367, 1439, 1487, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2879, 2903, 2999, 3023, 3119, 3167, 3203, 3467, 3623, 3779, 3863, 4007, 4079, 4127
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Subsequence of A005385.
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EXAMPLE
| For p = 2 (the only case with p+1 odd), 2*p+1 = 5 is prime but p+1 = 3 is squarefree, so 5 is not in the sequence. For p = 3, 2*p+1 = 7 is prime and p+1 = 4 is not squarefree, so 7 is in the sequence.
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MATHEMATICA
| << 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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PROG
| (MAGMA) [ q: p in PrimesUpTo(2100) | not IsSquarefree(p+1) and IsPrime(q) where q is 2*p+1 ];
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CROSSREFS
| Cf. A013929 (not squarefree numbers), A005385 (safe primes p: (p-1)/2 is also prime), A153207, A153208, A153209.
Sequence in context: A184882 A073577 A139830 * A185955 A158035 A101789
Adjacent sequences: A153207 A153208 A153209 * A153211 A153212 A153213
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 20 2008
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EXTENSIONS
| Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 24 2008
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