A176010 - OEIS

%I #24 Mar 28 2024 14:33:46

%S 14,83,111,180,208,277,305,374,402,471,499,568,596,665,693,762,790,

%T 859,887,956,984,1053,1081,1150,1178,1247,1275,1344,1372,1441,1469,

%U 1538,1566,1635,1663,1732,1760,1829,1857,1926,1954,2023,2051,2120,2148,2217

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

%H Vincenzo Librandi, <a href="/A176010/b176010.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = (-97 + 41*(-1)^n + 194*n)/4.

%F a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3; a(1)=14, a(2)=83, a(3)=111.

%F a(n) = a(n-1) + 69 for n even, a(n) = a(n-1) + 28 for n odd, a(1)=14.

%F G.f.: x*(14+69*x+14*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Aug 24 2011

%F Sum_{n>=1} (-1)^(n+1)/a(n) = cot(14*Pi/97)*Pi/97. - _Amiram Eldar_, Feb 28 2023

%t Table[(97-41*(-1)^(n-1)+194*(n-1))/4,{n,1,50}] (* _Vincenzo Librandi_, Jul 13 2012 *)

%t Select[Range[2500],PowerMod[#,2,97]==2&] (* or *) LinearRecurrence[{1,1,-1},{14,83,111},50] (* _Harvey P. Dale_, Mar 28 2024 *)

%o (Magma) [(-97+41*(-1)^n+194*n)/4: n in [1..50]]; // _Vincenzo Librandi_, Jul 13 2012

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Apr 06 2010