login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A172001 Nonsquare positive integers n such that Pell equation y^2 - n*x^2 = -1 has rational solutions but the norm of fundamental unit of quadratic field Q(sqrt(n)) is 1. 1
34, 136, 146, 178, 194, 205, 221, 305, 306, 377, 386, 410, 466, 482, 505, 514, 544, 545, 562, 584, 674, 689, 706, 712, 745, 776, 793, 802, 820, 850, 866, 884, 890, 898, 905, 1154, 1186, 1202, 1205, 1220, 1224, 1234, 1282, 1314, 1345, 1346, 1394, 1405, 1469 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If the fundamental unit y0 + x0*sqrt(n) of Q(sqrt(n)) has norm -1, then (x0,y0) represents a rational solution to Pell equation y^2 - n*x^2 = -1. For n in this sequence, rational solutions exist but not delivered by the fundamental unit.

The set difference of A000415 and A172000 (note that A172000 is a subsequence of A000415).

Also, the set difference of A087643 and A022544 (note that A022544 is a subsequence of A087643).

The squarefree elements form A031398.

LINKS

Table of n, a(n) for n=1..49.

FORMULA

A positive integer n is in this sequence iff its squarefree core A007913(n) belongs to A031398.

CROSSREFS

Sequence in context: A334648 A044366 A044747 * A303302 A158062 A141127

Adjacent sequences:  A171998 A171999 A172000 * A172002 A172003 A172004

KEYWORD

nonn

AUTHOR

Max Alekseyev, Jan 21 2010

EXTENSIONS

Edited by Max Alekseyev, Mar 09 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)