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Numbers X such that there exists Y in N : X^2=237*Y^2+79.
1

%I #24 Apr 14 2024 04:44:32

%S 3002,1369815602,625049598820802,285211382039759778602,

%T 130142524046881416896829002,59384294007354872910817107492002,

%U 27097172124013900694904786365918667602,12364493834472406620879088955430602756635802,5641943265630330913796356147845990112692511056602

%N Numbers X such that there exists Y in N : X^2=237*Y^2+79.

%H Vincenzo Librandi, <a href="/A145304/b145304.txt">Table of n, a(n) for n = 1..180</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (456302,-1).

%F a(n+2) = 456302*a(n+1)-a(n).

%F G.f.: -3002*x*(x-1)/(x^2-456302*x+1). [_Colin Barker_, Aug 24 2012]

%e a(1)=3002 because the first relation is 3002^2=237*195^2+79

%t LinearRecurrence[{456302,-1},{3002,1369815602},10] (* _Harvey P. Dale_, Feb 16 2014 *)

%t CoefficientList[Series[3002 (1 - x)/(x^2 - 456302 x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 18 2014 *)

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 06 2008

%E More terms from _Harvey P. Dale_, Feb 16 2014