cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A031397 #28 Mar 05 2019 08:58:21
%S A031397 50,125,250,325,338,425,845,925,1025,1250,1325,1445,1450,1525,1625,
%T A031397 1682,1825,1850,2050,2125,2197,2425,2725,2738,2825,2873,2890,3050,
%U A031397 3125,3250,3425,3625,3725,3925,4250,4325,4394,4625,4825,4901,4913
%N A031397 Nonsquarefree n such that Pell equation x^2 - n y^2 = -1 is soluble.
%D A031397 Harvey Cohn, Advanced Number Theory, Dover Publications, New York, N.Y. (1980).
%D A031397 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 A031397 Giovanni Resta, <a href="/A031397/b031397.txt">Table of n, a(n) for n = 1..10000</a> (first 500 terms from Robert Israel)
%p A031397 filter:= t -> not numtheory:-issqrfree(t) and [isolve(x^2 - t*y^2 = -1)]<>[]:
%p A031397 select(filter, [$1..10000]); # _Robert Israel_, Jul 10 2018
%t A031397 r[n_] := Reduce[x>0 && y>0 && x^2 - n y^2 == -1, {x, y}, Integers];
%t A031397 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 A031397 Equals {A003814} minus {A003654}, cf. A031396.
%K A031397 nonn
%O A031397 1,1
%A A031397 _David W. Wilson_
%E A031397 Offset changed by _Robert Israel_, Jul 10 2018