id:A056931 - OEIS Search Results

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Difference between n-th pronic [=n(n+1)] and average of smallest prime greater than n^2 and largest prime less than (n+1)^2.

+0
5

0, 0, 0, 0, 0, -1, -1, 0, 3, -1, -2, -1, 0, 1, 2, 1, -3, -2, 0, 1, 1, -4, 2, -2, 0, 3, -1, 0, 0, -2, -3, 0, -3, 0, 0, 0, 3, 0, 5, -4, -6, -5, -3, 0, -6, 1, -2, 6, 2, -2, 1, -2, 0, 1, 9, 0, 2, -2, -3, 2, -1, -9, 1, 1, 2, -1, -6, -6, -1, -3, 0, 0, 0, 6, -1, -3, 3, -2, -7, 1, -2, 1, 2, -1, -4 (list; graph; listen)

	OFFSET	`2,9`
	COMMENT	`a(1)=-0.5 which is not an integer`
	FORMULA	`a(n) =A002378(n)-(A007491(n)+A053001(n+1))/2 =A002378(n)-A056930(n).`
	EXAMPLE	`a(4)=0 because smallest prime greater than 4^2 is 17, largest prime less than 5^2 is 23, average of 17 and 23 is 20, and 4*5-20=0`
	MAPLE	`with(numtheory): A056931 := n-> n*(n+1)-(prevprime((n+1)^2)+nextprime(n^2))/2);`
	CROSSREFS	`Cf. A002378, A007491, A053000, A053001, A056927, A056928, A056929, A056930.` `Adjacent sequences: A056928 A056929 A056930 this_sequence A056932 A056933 A056934` `Sequence in context: A074090 A054025 A054869 this_sequence A139569 A086249 A016569`
	KEYWORD	`easy,sign`
	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 October 10 20:39 EDT 2008. Contains 144831 sequences.

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