A304875 - OEIS

%I #6 May 20 2018 11:30:38

%S 5,11,19,31,41,61,67,83,103,139,149,181,199,227,271,307,331,373,421,

%T 443,547,571,631,631,691,739,811,853,919,1039,1039,1091,1249,1237,

%U 1301,1447,1459,1531,1621,1693,1787,1867

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

%C 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.

%H Hugo Pfoertner, <a href="/A304875/b304875.txt">Table of n, a(n) for n = 2..10000</a>

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

%e a(2) = 5 because 2^2 = 4 = (3 + 5)/2,

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

%Y Cf. A172989, A304874.

%K nonn

%O 2,1

%A _Hugo Pfoertner_, May 20 2018