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.

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

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.

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

Set difference of A000415 and its subsequence A172000.

Set difference of A087643 and its subsequence A022544.

Squarefree terms form A031398.

Odd terms form A249052.

Cf. A031399, A137351.

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