id:A066927 - OEIS Search Results

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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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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; listen)

	OFFSET	`1,1`
	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: A068063 A087181 A034973 this_sequence A060065 A057356 A020913` `Adjacent sequences: A066924 A066925 A066926 this_sequence A066928 A066929 A066930`
	KEYWORD	`easy,nonn`
	AUTHOR	`Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 24 2002`

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.

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