OFFSET
1,3
COMMENTS
Values of k are in A240469.
EXAMPLE
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 4 is in sequence.
PROG
(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
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(res, ", "))) }
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Ralf Stephan, Apr 06 2014
STATUS
approved