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%I #10 May 20 2018 11:30:47
%S 3,7,13,19,31,37,61,79,97,103,139,157,193,223,241,271,317,349,379,439,
%T 421,487,521,619,661,719,757,829,881,883,1009,1087,1063,1213,1291,
%U 1291,1429,1511,1579,1669,1741,1831,1879
%N Greatest prime p1 < p2 such that n^2 = (p1 + p2)/2 and p2 is prime.
%C 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.
%H Hugo Pfoertner, <a href="/A304874/b304874.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = n^2 - A172989(n) = A304875(n) - 2*A172989(n).
%e a(2) = 3 because 2^2 = 4 = (3 + 5)/2,
%e 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.
%Y Cf. A172989, A304875.
%K nonn
%O 2,1
%A _Hugo Pfoertner_, May 20 2018
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