This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225195 #16 Jan 12 2019 19:33:01 %S A225195 3,7,61,79,139,223,317,439,619,1087,1669,2593,3593,4093,5179,6079, %T A225195 8461,12541,13687,16633,19037,19597,25261,27211,28219,29581,36857, %U A225195 38011,39199,45361,46649,47521,51977,56167,74527,87013,88801,91807,92413,95479,103681 %N A225195 Primes p such that (p+nextprime(p))/2 is a perfect square. %C A225195 Primes for which average of two consecutive primes is a perfect square. %H A225195 Charles R Greathouse IV, <a href="/A225195/b225195.txt">Table of n, a(n) for n = 1..5000</a> %e A225195 61 is in the list since (61+67)/2=64=8^2. %t A225195 Select[Prime[Range[10000]],IntegerQ[Sqrt[(# + NextPrime[#])/2]] &] %t A225195 Select[Partition[Prime[Range[10000]],2,1],IntegerQ[Sqrt[Mean[#]]]&][[All,1]] (* _Harvey P. Dale_, Jan 12 2019 *) %o A225195 (PARI) p=2;forprime(q=3,1e9,if(issquare((p+q)/2),print1(p", "));p=q) \\ _Charles R Greathouse IV_, May 09 2013 %Y A225195 Cf. A000040, A000290, A069495, A075190 %K A225195 nonn %O A225195 1,1 %A A225195 _Jayanta Basu_, May 09 2013