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

1,3

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]

Mathematica

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

Prog

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

Crossrefs

Cf. A053370-A053375.

Sequence in context: A342992 A119418 A077058 * A297733 A255812 A249141

Adjacent sequences: A053370 A053371 A053372 * A053374 A053375 A053376

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jan 06 2000

Status

approved