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%I #31 Jul 02 2023 18:31:25
%S 4,9,17,22,30,35,43,48,56,61,69,74,82,87,95,100,108,113,121,126,134,
%T 139,147,152,160,165,173,178,186,191,199,204,212,217,225,230,238,243,
%U 251,256,264,269,277,282,290,295,303,308,316,321,329,334,342,347,355,360
%N Numbers congruent to 4 or 9 mod 13.
%C Numbers k such that k^2 is congruent to 3 (modulo 13).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).
%F From _R. J. Mathar_, Apr 20 2009: (Start)
%F a(n) = a(n-2) + 13 = a(n-1) + a(n-2) - a(n-3) = 13*n/2 - 13/4 - 3*(-1)^n/4.
%F G.f.: x*(4+5*x+4*x^2)/((1+x)*(x-1)^2). (End)
%F a(n) = 13*(n-1) - a(n-1), (with a(1)=4). - _Vincenzo Librandi_, Nov 17 2010
%F Sum_{n>=1} (-1)^(n+1)/a(n) = tan(5*Pi/26)*Pi/13. - _Amiram Eldar_, Feb 27 2023
%t Select[Range[400],MemberQ[{4,9},Mod[#,13]]&] (* or *) Select[Range[400], PowerMod[#,2,13]==3&] (* _Harvey P. Dale_, Mar 05 2012 *)
%Y A127547 is a subsequence.
%K nonn
%O 1,1
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 25 2004
%E More terms from _Ray Chandler_, Mar 27 2004
%E Edited by _N. J. A. Sloane_, May 10 2007
%E Incorrect formula deleted by _N. J. A. Sloane_, Jun 16 2010
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