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 A214735 #25 Feb 14 2017 02:48:13
%S A214735 2,3,5,17,29,37,41,43,53,67,73,89,109,113,131,137,149,151,157,163,181,
%T A214735 197,199,229,233,241,277,293,313,317,331,337,349,367,373,389,401,409,
%U A214735 421,433,449,457,461,521,541,557,577,593,601,613,617,619,631,641,643
%N A214735 Primes such that no pairwise sum is a square.
%C A214735 a(n+1) is the smallest prime p > a(n) such that none of sums a(i)+p, i=1..n is a square.
%C A214735 The sequence is infinite.
%H A214735 Zak Seidov, <a href="/A214735/b214735.txt">Table of n, a(n) for n = 1..10000</a>
%e A214735 a(3) = 5 because 2 + 5 = 7 (not a square) and 3 + 5 = 8 (a cube, not a square).
%e A214735 7 is not in the sequence because 2 + 7 = 3^2. With 11, we have 11 + 5 = 4^2, and for 13, there is 3 + 13 = 4^2.
%e A214735 a(4) = 17, as 2 + 17 = 19 (a prime), 3 + 17 = 20 (divisible by a square but not itself a square) and 5 + 17 = 22 (a squarefree semiprime).
%t A214735 t = {2}; currPrime = 2; len = 1; maxLen = 100; Do[Label[ne]; currPrime = NextPrime[currPrime]; Do[If[IntegerQ[Sqrt[t[[i]] + currPrime]], Goto[ne]], {i, len}]; AppendTo[t, currPrime]; len++, {maxLen - 1}]; t
%o A214735 (PARI) list(lim)=my(v=List([2])); forprime(p=3,lim, if(issquare(p+2), next); for(k=sqrtint(p+2)+1,sqrtint(2*p-2), if(setsearch(v,k^2-p), next(2))); listput(v, p)); Vec(v) \\ _Charles R Greathouse IV_, Feb 14 2017
%Y A214735 Cf. A086086, A203988.
%K A214735 nonn
%O A214735 1,1
%A A214735 _Zak Seidov_, Jul 27 2012