This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113805 #26 Nov 27 2024 07:26:15
%S A113805 5,9,19,23,33,37,47,51,61,65,75,79,89,93,103,107,117,121,131,135,145,
%T A113805 149,159,163,173,177,187,191,201,205,215,219,229,233,243,247,257,261,
%U A113805 271,275,285,289,299,303,313,317,327,331,341,345,355,359,369
%N A113805 Numbers that are congruent to {5, 9} mod 14.
%F A113805 a(n) = 14*n - a(n-1) - 14 (with a(1) = 5). - _Vincenzo Librandi_, Nov 13 2010
%F A113805 From _Wolfdieter Lang_, Dec 15 2011: (Start)
%F A113805 a(n) = 7*n-(7+3*(-1)^n)/2.
%F A113805 O.g.f.: x*(5+4*x+5*x^2)/((1+x)*(1-x)^2).
%F A113805 See the _Bruno Berselli_ contribution under A113801. (End)
%F A113805 Sum_{n>=1} (-1)^(n+1)/a(n) = tan(Pi/7)*Pi/14. - _Amiram Eldar_, Dec 30 2021
%F A113805 From _Amiram Eldar_, Nov 25 2024: (Start)
%F A113805 Product_{n>=1} (1 - (-1)^n/a(n)) = 4*sin(Pi/7)*sin(3*Pi/14).
%F A113805 Product_{n>=1} (1 + (-1)^n/a(n)) = 2*sin(Pi/7). (End)
%t A113805 Flatten[Table[14n + {5, 9}, {n, 0, 28}]] (* _Alonso del Arte_, Dec 15 2011 *)
%Y A113805 Cf. A113801, A113802, A113803, A113804, A113806, A008589, A113807.
%K A113805 nonn,easy
%O A113805 1,1
%A A113805 _Giovanni Teofilatto_, Jan 22 2006