%I #32 Aug 26 2024 02:06:01

%S 5,7,17,19,29,31,41,43,53,55,65,67,77,79,89,91,101,103,113,115,125,

%T 127,137,139,149,151,161,163,173,175,185,187,197,199,209,211,221,223,

%U 233,235,245,247,257,259,269,271,281,283,293,295,305,307,317,319,329,331

%N Numbers that are congruent to {5, 7} (mod 12).

%D L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 64.

%H Amiram Eldar, <a href="/A092242/b092242.txt">Table of n, a(n) for n = 1..10000</a>

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

%F 1/5^2 + 1/7^2 + 1/17^2 + 1/19^2 + 1/29^2 + 1/31^2 + ... = Pi^2*(2 - sqrt(3))/36 = 0.073459792... [Jolley] - _Gary W. Adamson_, Dec 20 2006

%F a(n) = 12*n - a(n-1) - 12 (with a(1)=5). - _Vincenzo Librandi_, Nov 16 2010

%F From _R. J. Mathar_, Oct 08 2011: (Start)

%F a(n) = 6*n - 3 - 2*(-1)^n.

%F G.f.: x*(5+2*x+5*x^2) / ( (1+x)*(x-1)^2 ). (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = (2 - sqrt(3))*Pi/12. - _Amiram Eldar_, Dec 04 2021

%t Select[Range[331], MemberQ[{5, 7}, Mod[#, 12]] &] (* _Amiram Eldar_, Dec 04 2021 *)

%Y Fifth row of A092260.

%K nonn,easy

%O 1,1

%A _Giovanni Teofilatto_, Feb 19 2004

%E Edited and extended by _Ray Chandler_, Feb 21 2004