A056930 Average of smallest prime greater than n^2 and largest prime less than (n+1)^2.

6, 12, 20, 30, 42, 57, 73, 90, 107, 133, 158, 183, 210, 239, 270, 305, 345, 382, 420, 461, 505, 556, 598, 652, 702, 753, 813, 870, 930, 994, 1059, 1122, 1193, 1260, 1332, 1406, 1479, 1560, 1635, 1726, 1812, 1897, 1983, 2070, 2168, 2255, 2354, 2444

Offset: 2

Author

Henry Bottomley, Jul 12 2000

Keywords

• easy
• nonn

Comments

a(1)=2.5 which is not an integer

Examples

			a(4)=1 because smallest prime greater than 4^2 is 17, largest prime less than 5^2 is 23 and average of 17 and 23 is 20
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A002378, A007491, A053000, A053001, A056927, A056928, A056929, A056931.

Programs

Mathematica

Table[Mean[{NextPrime[n^2],NextPrime[(n+1)^2,-1]}],{n,2,50}] (* Harvey P. Dale, May 10 2019 *)

Formula

a(n) =(A007491(n)+A053001(n+1))/2 =A002378(n)-A056931(n)