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

1,1

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.

Links

Table of n, a(n) for n=1..48.

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) ;

Crossrefs

Cf. A130226.

Sequence in context: A369355 A034858 A249354 * A114290 A277912 A000531

Adjacent sequences: A249018 A249019 A249020 * A249022 A249023 A249024

Keyword

nonn

Author

R. J. Mathar, Oct 19 2014

Status

approved