A056929 Difference between n^2 and average of smallest prime greater than n^2 and largest prime less than n^2.

0, 0, 1, -1, 2, -1, 0, 0, 1, 1, 0, -1, 1, 0, 2, 1, 0, -2, 1, 0, 1, -3, 2, 0, 1, -1, 4, -5, 3, 1, -2, 0, -2, -1, 2, -1, 1, 4, 1, 0, -4, -5, -5, 3, -5, -1, 1, -4, 10, 0, 1, -2, 3, -5, 7, 9, -2, 1, 0, -2, 4, -9, 0, 1, 3, 1, -5, -10, 4, -4, 0, 1, 2, -6, 12, -4, 0, 3, -9, 3, -2, -2, 6, 1, -6, 2, -3

Offset: 2

Author

Henry Bottomley, Jul 12 2000

Keywords

• easy
• sign

Comments

Conjecture: the most frequent value will be 1 (including sequence variants with any even power n^2k). - Bill McEachen, Dec 12 2022

Examples

			a(4)=1 because smallest prime greater than 4^2 is 17, largest prime less than 4^2 is 13, average of 17 and 13 is 15 and 16-15=1.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A007491, A053000, A053001, A056927, A056928, A056930, A056931.

Programs

Maple

with(numtheory): A056929 := n-> n^2-(prevprime(n^2)+nextprime(n^2))/2);

Mathematica

Array[# - Mean@ {NextPrime[#], NextPrime[#, -1]} &[#^2] &, 87, 2] (* Michael De Vlieger, May 20 2018 *)

PARI

a(n) = n^2 - (nextprime(n^2) + precprime(n^2))/2; \\ Michel Marcus, May 20 2018

Formula

a(n) = A000290(n) - A056928(n).

a(n) = (A056927(n) - A053000(n))/2.

Extensions

More terms from James Sellers, Jul 13 2000