A031397 - OEIS

%I #28 Mar 05 2019 08:58:21

%S 50,125,250,325,338,425,845,925,1025,1250,1325,1445,1450,1525,1625,

%T 1682,1825,1850,2050,2125,2197,2425,2725,2738,2825,2873,2890,3050,

%U 3125,3250,3425,3625,3725,3925,4250,4325,4394,4625,4825,4901,4913

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

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

%D 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,

%H Giovanni Resta, <a href="/A031397/b031397.txt">Table of n, a(n) for n = 1..10000</a> (first 500 terms from Robert Israel)

%p filter:= t -> not numtheory:-issqrfree(t) and [isolve(x^2 - t*y^2 = -1)]<>[]:

%p select(filter, [$1..10000]); # _Robert Israel_, Jul 10 2018

%t r[n_] := Reduce[x>0 && y>0 && x^2 - n y^2 == -1, {x, y}, Integers];

%t 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 *)

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

%K nonn

%O 1,1

%A _David W. Wilson_

%E Offset changed by _Robert Israel_, Jul 10 2018