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A066927
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Least k such that between p and 2p, for all primes > 3, there is always a number that is twice a square, i.e.; a k such that p < 2k^2 < 2p.
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0
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2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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EXAMPLE
| a(5) = 3. The 5th prime is 11 and 2p is 22. The theorem says that there exists a number k, between p & 2p that is twice a square. 18 is between 11 & 22 and is of the form 2k^2, k being 3.
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MATHEMATICA
| Table[ Ceiling[ Sqrt[ Prime[ n ]/2 ] ], {n, 1, 100} ]
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CROSSREFS
| Cf. A006255.
Sequence in context: A068063 A087181 A034973 * A060065 A057356 A172274
Adjacent sequences: A066924 A066925 A066926 * A066928 A066929 A066930
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KEYWORD
| easy,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 24 2002
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