A304875 Least prime p2 > p1 such that n^2 = (p1 + p2)/2 and p1 is prime.

5, 11, 19, 31, 41, 61, 67, 83, 103, 139, 149, 181, 199, 227, 271, 307, 331, 373, 421, 443, 547, 571, 631, 631, 691, 739, 811, 853, 919, 1039, 1039, 1091, 1249, 1237, 1301, 1447, 1459, 1531, 1621, 1693, 1787, 1867

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 least prime p2 such that n^2 = (p1 + p2) / 2. The corresponding p1 is provided in A304874.

Examples

			a(2) = 5 because 2^2 = 4 = (3 + 5)/2,
a(7) = 61 because 7^2 = 49 = (37 + 61)/2 and p2 = 53 or p2 = 59 don't lead to a prime p1.
		

Links

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

Crossrefs

Cf. A172989, A304874.

Formula

a(n) = n^2 + A172989(n) = A304874(n) + 2*A172989(n).