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 A066927 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. 0
 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; text; internal format)
 OFFSET 1,1 LINKS 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. MATHEMATICA Table[ Ceiling[ Sqrt[ Prime[ n ]/2 ] ], {n, 1, 100} ] CROSSREFS Cf. A006255. Sequence in context: A034973 A316626 A269734 * A060065 A057356 A172274 Adjacent sequences:  A066924 A066925 A066926 * A066928 A066929 A066930 KEYWORD easy,nonn AUTHOR Robert G. Wilson v, Jan 24 2002 STATUS approved

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Last modified July 27 04:32 EDT 2021. Contains 346305 sequences. (Running on oeis4.)