OFFSET
1,1
REFERENCES
L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 64.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
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
a(n) = 12*n - a(n-1) - 12 (with a(1)=5). - Vincenzo Librandi, Nov 16 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 6*n - 3 - 2*(-1)^n.
G.f.: x*(5+2*x+5*x^2) / ( (1+x)*(x-1)^2 ). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (2 - sqrt(3))*Pi/12. - Amiram Eldar, Dec 04 2021
MATHEMATICA
Select[Range[331], MemberQ[{5, 7}, Mod[#, 12]] &] (* Amiram Eldar, Dec 04 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Feb 19 2004
EXTENSIONS
Edited and extended by Ray Chandler, Feb 21 2004
STATUS
approved