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

2,1

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.

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A172989, A304874.

Sequence in context: A191032 A003147 A106068 * A164566 A075322 A079850

Adjacent sequences: A304872 A304873 A304874 * A304876 A304877 A304878

Keyword

nonn

Author

Hugo Pfoertner, May 20 2018

Status

approved