id:A089332 - OEIS Search Results

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A constructed function that for the first thousand integers is near n over the range using consecutive squares in the prime distribution as the base.

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30, 15, 31, 17, 23, 10, 26, 13, 20, 17, 5, 22, 30, 7, 15, 12, 20, 18, 16, 4, 32, 20, 8, 16, 24, 12, 10, 28, 16, 25, 13, 21, 10, 8, 36, 25, 33, 21, 0, 28, 17, 35, 4, 32, 51, 0, 8, 47, 55, 14, 23, 1, 10, 59, 17, 46, 45, 13, 52, 31, 20, 38, 27, 26, 45, 3, 82, 21, 20, 39, 37, 46, 85, 4, 43, 92, -9, 60, 48, 57, 26, 15, 64, 73, 32, 31, 50, 49, 38 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Although larger at the beginning than n the sequence is bounded by n in the first 1000 and the result is chaotic in structure and only one value (-9) is negative. The function: f[n]=2*n/Sqrt[n]-4 contains the tendency of the consecutive squares in the prime distribution, but not their variability.`
	FORMULA	`a(n) = Floor[10(PrimePi[(n+1)^2]-PrimePi[n^2]-2n/Sqrt[n]+4)]`
	MATHEMATICA	`digits=5200 a=Table[Floor[10(PrimePi[(n+1)^2]-PrimePi[n^2]-2*n/Sqrt[n]+4)], {n, 4, digits}]`
	CROSSREFS	`Adjacent sequences: A089329 A089330 A089331 this_sequence A089333 A089334 A089335` `Sequence in context: A033350 A070293 A070657 this_sequence A040873 A070891 A033971`
	KEYWORD	`sign,uned`
	AUTHOR	`Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 03 2004`

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Last modified October 15 20:12 EDT 2008. Contains 145099 sequences.

AT&T Labs Research