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

2,1

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.

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A172989, A304875.

Sequence in context: A023220 A207990 A023205 * A167473 A256864 A231432

Adjacent sequences: A304871 A304872 A304873 * A304875 A304876 A304877

Keyword

nonn

Author

Hugo Pfoertner, May 20 2018

Status

approved