A031397 Nonsquarefree n such that Pell equation x^2 - n y^2 = -1 is soluble.

50, 125, 250, 325, 338, 425, 845, 925, 1025, 1250, 1325, 1445, 1450, 1525, 1625, 1682, 1825, 1850, 2050, 2125, 2197, 2425, 2725, 2738, 2825, 2873, 2890, 3050, 3125, 3250, 3425, 3625, 3725, 3925, 4250, 4325, 4394, 4625, 4825, 4901, 4913

Offset: 1

Author

David W. Wilson

Keywords

• nonn

References

• Harvey Cohn, Advanced Number Theory, Dover Publications, New York, N.Y. (1980).
• 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

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 500 terms from Robert Israel)

Crossrefs

Equals {A003814} minus {A003654}, cf. A031396.

Programs

Maple

filter:= t -> not numtheory:-issqrfree(t) and [isolve(x^2 - t*y^2 = -1)]<>[]:
select(filter, [$1..10000]); # Robert Israel, Jul 10 2018

Mathematica

r[n_] := Reduce[x>0 && y>0 && x^2 - n y^2 == -1, {x, y}, Integers];
Reap[For[n = 1, n <= 5000, n++, If[!SquareFreeQ[n], If[r[n] =!= False, Print[n]; Sow[n]]]]][[2, 1]] (* Jean-François Alcover, Mar 05 2019 *)

Extensions

Offset changed by Robert Israel, Jul 10 2018