%I #29 Feb 26 2023 04:24:50

%S 17,24,58,65,99,106,140,147,181,188,222,229,263,270,304,311,345,352,

%T 386,393,427,434,468,475,509,516,550,557,591,598,632,639,673,680,714,

%U 721,755,762,796,803,837,844,878,885,919,926,960,967,1001,1008,1042,1049

%N Numbers k such that k^2 == 2 (mod 41).

%C Numbers congruent to {17, 24} mod 41. - _Amiram Eldar_, Feb 26 2023

%H Vincenzo Librandi, <a href="/A158803/b158803.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) = a(n-1) + a(n-2) - a(n-3).

%F a(n) = (1/4)*(41 + 27*(-1)^(n-1) + 82*(n-1)).

%F First differences: a(2n) - a(2n-1) = 7, a(2n+1) - a(2n) = 34.

%F G.f.: x*(17 + 7*x + 17*x^2)/((1+x)*(x-1)^2). - _R. J. Mathar_, Apr 04 2009

%F Sum_{n>=1} (-1)^(n+1)/a(n) = tan(7*Pi/82)*Pi/41. - _Amiram Eldar_, Feb 26 2023

%t LinearRecurrence[{1, 1, -1}, {17, 24, 58}, 60] (* _Vincenzo Librandi_, Mar 02 2012 *)

%t Select[Range[1200],PowerMod[#,2,41]==2&] (* _Harvey P. Dale_, Oct 24 2021 *)

%o (Magma) I:=[17, 24, 58]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // _Vincenzo Librandi_, Mar 02 2012

%o (PARI) a(n) = (1/4)*(41+27*(-1)^(n-1)+82*(n-1)); \\ _Vincenzo Librandi_, Mar 02 2012

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 27 2009

%E Comments translated to formulas by _R. J. Mathar_, Apr 04 2009