A053373 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of y for n == 1 (mod 4).

1, 1, 2, 1, 1, 8, 2, 10, 1, 40, 5, 2, 3, 250, 1, 1, 106, 3, 1138, 2, 8, 25, 146, 2968, 15, 298, 16, 2, 5, 17, 1856, 1, 1, 9384, 97, 10, 253970, 2, 72664, 3, 6440, 5, 521904, 1, 1, 3034, 5, 9148450, 1084152, 117, 2, 746, 10, 88, 157, 126890, 1, 1, 1311, 56, 287

Offset: 1

Author

N. J. A. Sloane, Jan 06 2000

Keywords

• nonn
• easy
• nice

Comments

Entries are indexed by values of n from A039955.

Subsequence of A077058 excluding terms for which A077425(n) is not squarefree. - Max Alekseyev, Dec 12 2012

References

• R. A. Mollin, Quadratics, CRC Press, 1996, Tables B1-B3.

Links

• Emmanuel Vantieghem, Table of n, a(n) for n=1..1000
• S. R. Finch, Class number theory
• Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Crossrefs

Cf. A053370-A053375.

Programs

Mathematica

2*NumberFieldFundamentalUnits[ Sqrt[#] ][[1, 2, 2]] & /@ Select[ Range[5, 309, 4], SquareFreeQ ]  (* Jean-François Alcover, Jul 09 2013 *)

PARI

forstep(n=5,1000,4, if(!issquarefree(n),next); print1( 2*polcoeff(lift(bnfinit(x^2-n).fu[1]),1), ", " )) /* Max Alekseyev */