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A240469 Values k where the maximum number of distinct rational solutions to x^2 - Dy^2 = t, 0 < D <= k, 0 < t <= k, achieves a new record.

%I A240469 #13 Mar 25 2018 08:35:19
%S A240469 1,2,7,10,17,32,73,144,241,336,360,720,1080,1260
%N A240469 Values k where the maximum number of distinct rational solutions to x^2 - Dy^2 = t, 0 < D <= k, 0 < t <= k, achieves a new record.
%C A240469 Record values are in A240470.
%e A240469 All Diophantine equations x^2 - Dy^2 = t, 0 < D <= 16, 0 < t <= 16, D squarefree, have fewer than 4 distinct solutions; the first with 4 solutions is x^2 - 17y^2 = 16 with the solutions (x,y) = (9/2,1/2), (21,5), (4,0), (13,3), so 17 is in the sequence.
%o A240469 (PARI) { r(l,k)=if(!issquarefree(l)||!polisirreducible(z^2-l),return(0));v=bnfisintnorm(bnfinit(z^2-l), k);if(!#v,return(0));s=0;for(k=1,#v,p=v[k];a=polcoeff(p,0);b=polcoeff(p,1);f=1;for(l=k+1,#v,p=v[l];aa=polcoeff(p,0);bb=polcoeff(p,1);if(abs(a)==abs(aa)&&abs(b)==abs(bb),f=0;break));s=s+f);s
%o A240469 m=0;n=0;while(1,n=n+1;res=0;for(l=1,n,rr=r(l,n);if(rr>res,res=rr));for(k=1,n-1,rr=r(n,k);if(rr>res,res=rr));if(res>m,m=res;print(n,","))) }
%Y A240469 Cf. A218459, A077428, A035251, A031363.
%K A240469 nonn,more
%O A240469 1,2
%A A240469 _Ralf Stephan_, Apr 06 2014