%I #31 Jul 11 2022 16:04:39

%S 9,17,25,29,37,49,65,73,85,89,97,109,121,145,149,157,169,185,193,205,

%T 229,241,265,269,277,289,325,349,361,409,425,433,445,481,485,493,505,

%U 529,541,565,601,625,661,685,689,697,709,745,769,829,841,845,853,865

%N Numbers of the form (p^2 + q^2)/2, for odd primes p and q.

%C The primes in this sequence are listed in A103739.

%C a(n) mod 4 = 1. See A227697 for related sequence. - _Richard R. Forberg_, Sep 22 2013

%C The squares of primes in this sequence form the subsequence A001248 \ {4}. - _Bernard Schott_, Jul 09 2022

%H T. D. Noe, <a href="/A143850/b143850.txt">Table of n, a(n) for n = 1..1000</a>

%t Take[Union[Total[#]/2&/@(Tuples[Prime[Range[2,20]],2]^2)],60] (* _Harvey P. Dale_, Dec 28 2014 *)

%o (PARI) list(lim)=my(v=List(), p2); lim\=1; if(lim<9, lim=8); forprime(p=3, sqrtint(2*lim-9), p2=p^2; forprime(q=3, min(sqrtint(2*lim-p2), p), listput(v, (p2+q^2)/2))); Set(v) \\ _Charles R Greathouse IV_, Feb 14 2017

%Y Cf. A001248, A045636, A103739, A227697.

%Y Cf. A075892 (a subsequence).

%K nonn

%O 1,1

%A _T. D. Noe_, Sep 03 2008