id:A056927 - OEIS Search Results

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Difference between n^2 and largest prime less than n^2.

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1, 2, 3, 2, 5, 2, 3, 2, 3, 8, 5, 2, 3, 2, 5, 6, 7, 2, 3, 2, 5, 6, 5, 6, 3, 2, 11, 2, 13, 8, 3, 2, 3, 2, 5, 2, 5, 10, 3, 12, 5, 2, 3, 8, 3, 2, 7, 2, 23, 8, 5, 6, 7, 2, 15, 20, 3, 12, 7, 2, 11, 2, 3, 6, 7, 6, 3, 2, 11, 2, 5, 6, 5, 2, 27, 2, 5, 12, 3, 8, 5, 6, 13, 6, 3, 8, 3, 2, 7, 8, 3, 2, 5, 12, 7, 6, 3 (list; graph; listen)

	OFFSET	`2,2`
	COMMENT	`Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2 is equivalent to conjecturing that a(n)<2n-1 for all n>1`
	LINKS	`T. D. Noe, Table of n, a(n) for n=2..10000`
	FORMULA	`a(n) =A000290(n)-A053001(n)`
	EXAMPLE	`a(4)=3 because largest prime less than 4^2 is 13 and 16-13=3`
	MAPLE	`with(numtheory): A056927 := n-> n^2-prevprime(n^2);`
	CROSSREFS	`Cf. A053001, A056929, A056931.` `Sequence in context: A093476 A066727 A076606 this_sequence A094290 A101876 A087986` `Adjacent sequences: A056924 A056925 A056926 this_sequence A056928 A056929 A056930`
	KEYWORD	`easy,nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Jul 12 2000`
	EXTENSIONS	`More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 13 2000`

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Last modified September 5 17:15 EDT 2008. Contains 143476 sequences.

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