A238240 - OEIS

%I #15 Oct 22 2024 18:33:27

%S 18,35,50,63,72,74,83,90,95,98,99,107,140,162,171,200,215,227,252,266,

%T 275,288,296,315,332,347,359,360,362,371,380,387,392,395,396,407,428,

%U 450,491,495,530,539,560,567,602,623,626,635,648,666,684,695,711,722,743,747,755,770,791,794,800,810

%N Positive integers n such that x^2 - 20xy + y^2 + n = 0 has integer solutions.

%C Positive integers n such that  x^2 - 99 y^2 + n = 0 has integer solutions. - _Robert Israel_, Oct 22 2024

%H Robert Israel, <a href="/A238240/b238240.txt">Table of n, a(n) for n = 1..10000</a>

%e 63 is in the sequence because x^2 - 20xy + y^2 + 63 = 0 has integer solutions, for example (x, y) = (1, 16).

%p filter:= t -> [isolve(99*y^2 - z^2 = t)] <> []:

%p select(filter, [$1..1000]); # _Robert Israel_, Oct 22 2024

%Y Cf. A075839 (n = 18), A221763 (n = 63), A198947 (n = 90), A001085 (n = 99).

%Y Cf. A031363, A084917, A237351, A237599, A237606, A237609, A237610, A236330, A236331.

%K nonn

%O 1,1

%A _Colin Barker_, Feb 20 2014

%E Corrected by _Robert Israel_, Oct 22 2024