A056931 Difference between n-th oblong (promic) number, n(n+1), and the average of the smallest prime greater than n^2 and the largest prime less than (n+1)^2.

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

Offset: 2

Author

Henry Bottomley, Jul 12 2000

Keywords

• easy
• sign

Comments

a(1)=-0.5 which is not an integer

Examples

			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
		

Crossrefs

Cf. A002378, A007491, A053000, A053001, A056927, A056928, A056929, A056930.

Programs

Maple

with(numtheory): A056931 := n-> n*(n+1)-(prevprime((n+1)^2)+nextprime(n^2))/2);

Formula

a(n) =A002378(n)-(A007491(n)+A053001(n+1))/2 =A002378(n)-A056930(n).

Extensions

More terms from James Sellers, Jul 13 2000