A056928 Average of the smallest prime greater than n^2 and the largest prime less than n^2.

4, 9, 15, 26, 34, 50, 64, 81, 99, 120, 144, 170, 195, 225, 254, 288, 324, 363, 399, 441, 483, 532, 574, 625, 675, 730, 780, 846, 897, 960, 1026, 1089, 1158, 1226, 1294, 1370, 1443, 1517, 1599, 1681, 1768, 1854, 1941, 2022, 2121, 2210, 2303, 2405, 2490

Offset: 2

Author

Henry Bottomley, Jul 12 2000

Keywords

• easy
• nonn

Examples

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

Links

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

Crossrefs

Cf. A007491, A053000, A053001, A056927, A056929, A056930, A056931.

Programs

Mathematica

Table[n2=n^2;(NextPrime[n2,-1]+NextPrime[n2])/2,{n,2,100}] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)

PARI

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

Formula

a(n) = (A007491(n) - A053001(n))/2.

a(n) = A000290(n) + (A053000(n) - A056927(n))/2.

a(n) = A000290(n) - A056929(n).