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%I #33 Feb 26 2023 02:35:44
%S 9,32,50,73,91,114,132,155,173,196,214,237,255,278,296,319,337,360,
%T 378,401,419,442,460,483,501,524,542,565,583,606,624,647,665,688,706,
%U 729,747,770,788,811,829,852,870,893,911,934,952,975,993,1016,1034,1057
%N Numbers k such that k^2 == -1 (mod 41).
%C Numbers k such that k == 9 or 32 (mod 41). - _Charles R Greathouse IV_, Dec 27 2011
%H Vincenzo Librandi, <a href="/A155098/b155098.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 From _M. F. Hasler_, Jun 16 2010: (Start)
%F a(n) = 9*(-1)^(n+1) + 41*floor(n/2).
%F a(2k+1) = 41*k + a(1), a(2k) = 41*k - a(1), with a(1) = A002314(6) since 41 = A002144(6).
%F a(n) = a(n-2) + 41 for all n > 2. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = cot(9*Pi/41)*Pi/41. - _Amiram Eldar_, Feb 26 2023
%t LinearRecurrence[{1,1,-1},{9,32,50},100] (* _Vincenzo Librandi_, Feb 29 2012 *)
%t Select[Range[1100], PowerMod[#, 2, 41] == 40 &] (* _Vincenzo Librandi_, Apr 24 2014 *)
%o (PARI) A155098(n)=n\2*41-9*(-1)^n /* _M. F. Hasler_, Jun 16 2010 */
%Y Cf. A002144, A155086, A155095, A155096, A155097.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Jan 20 2009
%E Terms checked & minor edits by _M. F. Hasler_, Jun 16 2010
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