A031399 -id:A031399 - cp's OEIS frontend

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

Max Alekseyev, Jan 21 2010

nonn

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.

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.

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

Edited by Max Alekseyev, Mar 09 2010

A249052 Odd numbers n without prime factors of the form 4k+3 such that x^2-n*y^2=-1 has no solutions.

Original entry on oeis.org

205, 221, 305, 377, 505, 545, 689, 725, 745, 793, 905, 1205, 1345, 1405, 1469, 1513, 1517, 1537, 1717, 1885, 1945, 1961, 2005, 2041, 2045, 2105, 2225, 2245, 2329, 2353, 2525, 2533, 2669, 2701, 2845, 2993, 3005, 3205, 3305, 3497, 3505, 3737, 3757, 3805, 3893, 3965, 4069, 4105, 4145, 4205, 4321, 4369

Offset: 1

Joerg Arndt, Apr 09 2008

nonn

A positive odd integer n is in this sequence iff its squarefree core A007913(n) belongs to A031398. - Max Alekseyev, Jun 26 2022

Odd terms of A172001.

Cf. A031398, A031399, A137351.

cp's OEIS Frontend

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.

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