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A176010 Positive numbers k such that k^2 == 2 (mod 97).

%I A176010 #24 Mar 28 2024 14:33:46
%S A176010 14,83,111,180,208,277,305,374,402,471,499,568,596,665,693,762,790,
%T A176010 859,887,956,984,1053,1081,1150,1178,1247,1275,1344,1372,1441,1469,
%U A176010 1538,1566,1635,1663,1732,1760,1829,1857,1926,1954,2023,2051,2120,2148,2217
%N A176010 Positive numbers k such that k^2 == 2 (mod 97).
%H A176010 Vincenzo Librandi, <a href="/A176010/b176010.txt">Table of n, a(n) for n = 1..1000</a>
%H A176010 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A176010 a(n) = (-97 + 41*(-1)^n + 194*n)/4.
%F A176010 a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3; a(1)=14, a(2)=83, a(3)=111.
%F A176010 a(n) = a(n-1) + 69 for n even, a(n) = a(n-1) + 28 for n odd, a(1)=14.
%F A176010 G.f.: x*(14+69*x+14*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Aug 24 2011
%F A176010 Sum_{n>=1} (-1)^(n+1)/a(n) = cot(14*Pi/97)*Pi/97. - _Amiram Eldar_, Feb 28 2023
%t A176010 Table[(97-41*(-1)^(n-1)+194*(n-1))/4,{n,1,50}] (* _Vincenzo Librandi_, Jul 13 2012 *)
%t A176010 Select[Range[2500],PowerMod[#,2,97]==2&] (* or *) LinearRecurrence[{1,1,-1},{14,83,111},50] (* _Harvey P. Dale_, Mar 28 2024 *)
%o A176010 (Magma) [(-97+41*(-1)^n+194*n)/4: n in [1..50]]; // _Vincenzo Librandi_, Jul 13 2012
%K A176010 nonn,easy
%O A176010 1,1
%A A176010 _Vincenzo Librandi_, Apr 06 2010