OFFSET
1,1
COMMENTS
Numbers k such that k^2 is congruent to 3 (modulo 13).
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).
FORMULA
From R. J. Mathar, Apr 20 2009: (Start)
a(n) = a(n-2) + 13 = a(n-1) + a(n-2) - a(n-3) = 13*n/2 - 13/4 - 3*(-1)^n/4.
G.f.: x*(4+5*x+4*x^2)/((1+x)*(x-1)^2). (End)
a(n) = 13*(n-1) - a(n-1), (with a(1)=4). - Vincenzo Librandi, Nov 17 2010
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(5*Pi/26)*Pi/13. - Amiram Eldar, Feb 27 2023
MATHEMATICA
Select[Range[400], MemberQ[{4, 9}, Mod[#, 13]]&] (* or *) Select[Range[400], PowerMod[#, 2, 13]==3&] (* Harvey P. Dale, Mar 05 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 25 2004
EXTENSIONS
More terms from Ray Chandler, Mar 27 2004
Edited by N. J. A. Sloane, May 10 2007
Incorrect formula deleted by N. J. A. Sloane, Jun 16 2010
STATUS
approved