

A031398


Squarefree n with no 4k+3 factors such that Pell equation x^2  n y^2 = 1 is insoluble.


7



34, 146, 178, 194, 205, 221, 305, 377, 386, 410, 466, 482, 505, 514, 545, 562, 674, 689, 706, 745, 793, 802, 866, 890, 898, 905, 1154, 1186, 1202, 1205, 1234, 1282, 1345, 1346, 1394, 1405, 1469, 1513, 1517, 1537, 1538, 1717, 1762, 1802, 1858
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OFFSET

1,1


COMMENTS

Or, numbers n which are the sum of two relativelyprime squares but for which x^2  n*y^2 does not represent 1.
Together with {1} and A003654 forms a disjoint partition of A020893. That is, A020893 = {1} U A003654 U A031398. [From Max Alekseyev, Mar 09 2010]


REFERENCES

Harvey Cohn, "Advanced Number Theory".
J. P. Robertson and K. R. Matthews, A continued fraction approach to a result of Feit, Amer. Math. Monthly, 115 (No. 4, 2008), 346349.
S Vidhyalakshmi, V Krithika, K Agalya, On The Negative Pell Equation, International Journal of Emerging Technologies in Engineering Research (IJETER), Volume 4, Issue 2, February (2016) www.ijeter.everscience.org,


LINKS

JeanFrançois Alcover, Table of n, a(n) for n = 1..1000


MATHEMATICA

sel = Select[Range[2000], SquareFreeQ[#] && FreeQ[Mod[FactorInteger[#][[All, 1]], 4], 3]&]; r[n_] := Reduce[x^2n*y^2 == 1, {x, y}, Integers]; Reap[For[n=1, n <= Length[sel], n++, an = sel[[n]]; If[r[an] === False, Print[an]; Sow[an]]]][[2, 1]] (* JeanFrançois Alcover, Feb 04 2014 *)


CROSSREFS

Cf. A031396, A031397.
Sequence in context: A280550 A105714 A072319 * A259954 A180759 A159744
Adjacent sequences: A031395 A031396 A031397 * A031399 A031400 A031401


KEYWORD

nonn,changed


AUTHOR

David W. Wilson


EXTENSIONS

Edited by N. J. A. Sloane, Apr 28 2008, at the suggestion of Artur Jasinski.


STATUS

approved



