A053375 -id:A053375 - cp's OEIS frontend

A053370 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of x for n == 1 mod 4.

0, 1, 3, 2, 2, 19, 5, 27, 3, 131, 17, 7, 11, 943, 4, 4, 447, 13, 5035, 9, 37, 118, 703, 15371, 79, 1595, 87, 11, 28, 98, 10847, 6, 6, 57731, 604, 63, 1637147, 13, 478763, 20, 43331, 34, 3583111, 7, 7, 21639, 36, 66436843, 8011739, 872, 15, 5699, 77

Offset: 0

N. J. A. Sloane, Jan 06 2000

Entries are indexed by values of n from A039955.

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

S. R. Finch, Class number theory
Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Cf. A053370-A053375.

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).

Original entry on oeis.org

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

N. J. A. Sloane, Jan 06 2000

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

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

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]

Cf. A053370-A053375.

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

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

A053371 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of x for n == 2 mod 4.

Original entry on oeis.org

1, 5, 3, 15, 197, 5, 11, 35, 37, 13, 24335, 99, 63, 65, 251, 43, 53, 9, 10405, 2143295, 101, 4005, 21, 1025, 306917, 11, 57, 145925, 47, 143, 145, 21295, 7743, 1700902565, 13, 1451, 1601, 27, 7501, 52021, 195, 3141, 59535, 29

Offset: 0

N. J. A. Sloane, Jan 06 2000

Entries are indexed by values of n from A039956.

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

S. R. Finch, Class number theory
Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Cf. A053370-A053375.

NumberFieldFundamentalUnits[ Sqrt[#] ][[1, 2, 1]] & /@ Select[Range[2, 210, 2], SquareFreeQ] (* Jean-François Alcover, Jul 09 2013 *)

A053372 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of x for n == 3 mod 4.

Original entry on oeis.org

2, 8, 10, 4, 170, 24, 1520, 6, 25, 3482, 48, 50, 89, 530, 48842, 3480, 80, 82, 28, 1574, 39, 227528, 962, 295, 1126, 120, 122, 4730624, 10610, 77563250, 12, 1728148040, 249, 1324, 64080026, 168, 4190210, 487, 1682, 8994000, 14

Offset: 0

N. J. A. Sloane, Jan 06 2000

Entries are indexed by values of n from A039957.

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

S. R. Finch, Class number theory
Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Cf. A053370-A053375.

NumberFieldFundamentalUnits[ Sqrt[#] ][[1, 2, 1]] & /@ Select[Range[3, 195, 4], SquareFreeQ ] (* Jean-François Alcover, Jul 09 2013 *)

A053374 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of y for n == 2 mod 4.

Original entry on oeis.org

1, 2, 1, 4, 42, 1, 2, 6, 6, 2, 3588, 13, 8, 8, 30, 5, 6, 1, 1122, 221064, 10, 389, 2, 96, 28254, 1, 5, 12606, 4, 12, 12, 1716, 616, 132015642, 1, 110, 120, 2, 550, 3774, 14, 221, 4148, 2, 47533775646, 17, 10, 1, 6, 756, 5662, 16, 16, 6485718, 42, 85, 150

Offset: 0

N. J. A. Sloane, Jan 06 2000

Entries are indexed by values of n from A039956.

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

S. R. Finch, Class number theory
Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Cf. A053370-A053375.

sf = Select[2*Range[0, 139], SquareFreeQ]; NumberFieldFundamentalUnits[Sqrt[#]][[1, 2, 2]]& /@ sf (* Jean-François Alcover, May 31 2013 *)

cp's OEIS Frontend

A053370 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of x for n == 1 mod 4.

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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).

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A053371 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of x for n == 2 mod 4.

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A053372 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of x for n == 3 mod 4.

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Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

A053374 Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of y for n == 2 mod 4.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica