A249021 Value x in the solution of x^2-D*y^2=-1 as D runs through A003654.

7, 38, 117, 18, 268, 515, 70, 882, 32, 182, 99, 29718, 2072, 1068, 43, 2943, 378, 500, 5604, 4030, 4005, 8890182, 776, 5357, 57, 1744, 6948, 113582, 4832118, 8827, 1118, 1111225770, 68, 1764132, 11018, 3141, 251, 13545, 1710, 23156, 71011068, 16432, 6072, 82, 1407, 8920484118, 1063532, 19703

Offset: 1

Author

R. J. Mathar, Oct 19 2014

Keywords

• nonn

Comments

The pair (x,y) is taken from the numerator of the earliest (lowest order) convergent to the continued fraction of sqrt(D) that satisfies the "non-Pell" equation.

Crossrefs

Cf. A130226.

Programs

Maple

A249021 := proc(n)
    local dis,cf,o,q,x,y ;
    dis := A003654(n) ;
    cf := numtheory[cfrac](sqrt(dis),'periodic','quotients') ;
    for o from 1 do
        q := numtheory[nthconver](cf,o) ;
        x := numer(q) ;
        y := denom(q) ;
        if x^2-dis*y^2 = -1 then
            return x ;
        end if;
    end do:
end proc:
seq(A249021(n),n=1..50) ;