The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A194366 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A194366

Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1 and can be written as x+y*sqrt(d) with integers x, y where d is the squarefree part of n.
(history; published version)

#34 by Susanna Cuyler at Sun May 09 11:20:25 EDT 2021

STATUS

proposed

approved

#33 by Jon E. Schoenfield at Sun May 09 11:03:49 EDT 2021

STATUS

editing

proposed

#32 by Jon E. Schoenfield at Sun May 09 11:03:47 EDT 2021

COMMENTS

This sequence is a subset subsequence of A087643.

EXAMPLE

35 belong belongs to this sequence because x^2 + 35*y^2 = 1 have has the integer solution: x=6, y=1.

STATUS

approved

editing

#31 by N. J. A. Sloane at Mon Mar 06 11:25:48 EST 2017

STATUS

editing

approved

#30 by N. J. A. Sloane at Mon Mar 06 11:25:45 EST 2017

NAME

Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1 and can be written as x+y*sqrt(d) with integers x, y where two parts d is the squarefree part of fundamental unit are integersn.

COMMENTS

This sequence is a subset of A087643.

EXTENSIONS

Definition clarified by Emmanuel Vantieghem, Mar 06 2017

STATUS

approved

editing

#29 by N. J. A. Sloane at Mon Mar 06 11:23:56 EST 2017

STATUS

editing

approved

#28 by N. J. A. Sloane at Mon Mar 06 11:23:52 EST 2017

NAME

Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1 and can be written as x+y*sqrt(d) with integers x, y where two parts of fundamental unit are integers.

STATUS

proposed

editing

#27 by Emmanuel Vantieghem at Mon Mar 06 09:54:44 EST 2017

STATUS

editing

proposed

Discussion

Mon Mar 06

10:06

Emmanuel Vantieghem: In my discussion I may not use  sqrt(n) : this should be : sqrt(d), where d is the squarefree part of n.

#26 by Emmanuel Vantieghem at Mon Mar 06 09:50:06 EST 2017

NAME

Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(dn))has norm 1 and two parts of fundamental unit are integers.

STATUS

approved

editing

Discussion

Mon Mar 06

09:54

Emmanuel Vantieghem: I think that the expression "two parts of fundamental unit are integers" could be clarified.  I suggest "and can be written as  x+y*sqrt(n) with integers x, y".

#25 by Russ Cox at Sat Mar 31 10:22:18 EDT 2012

AUTHOR

_Artur Jasinski (grafix(AT)csl.pl), _, Oct 10 2011

Discussion

Sat Mar 31

10:22

OEIS Server: https://oeis.org/edit/global/339