login
A092242
Numbers that are congruent to {5, 7} (mod 12).
3
5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 89, 91, 101, 103, 113, 115, 125, 127, 137, 139, 149, 151, 161, 163, 173, 175, 185, 187, 197, 199, 209, 211, 221, 223, 233, 235, 245, 247, 257, 259, 269, 271, 281, 283, 293, 295, 305, 307, 317, 319, 329, 331
OFFSET
1,1
REFERENCES
L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 64.
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
Fifth row of A092260.
Sequence in context: A099389 A099382 A163633 * A003630 A122565 A369105
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Feb 19 2004
EXTENSIONS
Edited and extended by Ray Chandler, Feb 21 2004
STATUS
approved