A304874 Greatest prime p1 < p2 such that n^2 = (p1 + p2)/2 and p2 is prime.

3, 7, 13, 19, 31, 37, 61, 79, 97, 103, 139, 157, 193, 223, 241, 271, 317, 349, 379, 439, 421, 487, 521, 619, 661, 719, 757, 829, 881, 883, 1009, 1087, 1063, 1213, 1291, 1291, 1429, 1511, 1579, 1669, 1741, 1831, 1879

Offset: 2

Author

Hugo Pfoertner, May 20 2018

Keywords

• nonn

Comments

Each square > 1 can be written as the average of 2 primes p1 < p2. a(n) gives the greatest prime p1 such that n^2 = (p1 + p2) / 2. The corresponding p2 is provided in A304875.

Examples

			a(2) = 3 because 2^2 = 4 = (3 + 5)/2,
a(7) = 37 because 7^2 = 49 = (37 + 61)/2 and none of the primes p1 = 41, 43 or 47 leads to a prime p2.
		

Links

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

Crossrefs

Cf. A172989, A304875.

Formula

a(n) = n^2 - A172989(n) = A304875(n) - 2*A172989(n).